hello anons, very original thread idea prove to me that 0.999... is equal to 1. ive seen alot of threads about this topic pass around but ive never seen an actual conclusive answer.

File: 7 KB, 192x166, download.jpg [View same] [iqdb] [saucenao] [google]

Anonymous Fri Mar 27 22:26:11 2020 No.11507816 [Reply] [Original]

hello anons, very original thread idea
prove to me that 0.999... is equal to 1.
ive seen alot of threads about this topic pass around but ive never seen an actual conclusive answer.

>>	Anonymous Fri Mar 27 22:38:24 2020 No.11507839 10x=9.99999... - x=0.99999... —————————— 9x=9 x=1 If x=0.999... and x=1 then 0.999...=1

>>	Anonymous Fri Mar 27 22:46:32 2020 No.11507860 3/3 = 1 As is demonstrated in your pic, .999... = 3/3 Therefore .999... = 1 :)

Anonymous Fri Mar 27 23:00:20 2020 No.11507884

>>11507816
If the picture you posted doesn't convince you I have nothing to say because there's no way of putting it in simpler terms
You're just stubborn
1) decompose 0.999... in fractional form
2) get 3/3
What does a/a ALWAYS equal to when a∈R and a≠0?

>>	Anonymous Fri Mar 27 23:01:47 2020 No.11507887 >>11507816 You wouldn't understand the proof anyways. This thread is a troll and waste of time.

>>	Anonymous Fri Mar 27 23:04:11 2020 No.11507894 >>11507884 Not stubborn, I had always thought that it was equal to 1 but some people say the weirdest shit just to not make it equal 1. >>11507887 show us the proof bigman

>>	Anonymous Fri Mar 27 23:09:08 2020 No.11507902 >>11507816 shitty thread https://en.wikipedia.org/wiki/0.999......

>>	Anonymous Fri Mar 27 23:20:32 2020 No.11507916 >>11507816 You will never see proof that 0.99 equals 1, because it's a religious belief.

>>	Anonymous Fri Mar 27 23:30:18 2020 No.11507925 >>11507816 Does this mean that you can't truly divide something into perfect thirds? One piece will always be .00000000000000000000000000000000000~1 more than the other two pieces

>>	Anonymous Fri Mar 27 23:36:36 2020 No.11507933 >>11507925 the world is not constrained by our base ten number system

>>	Anonymous Fri Mar 27 23:57:48 2020 No.11507960 >>11507933 probably the the best response of the thread

Anonymous Sat Mar 28 00:03:12 2020 No.11507972

>>11507933
I mean to divide something into perfect thirfs outside of abstractly is seemingly impossible. How woukd you assure you have the same number of atoms or electrons. I guess you could seperate three electrons or something really small, but anything large would be hard

Anonymous Sat Mar 28 00:09:27 2020 No.11507985

This is how I make sense of it in my head so it's not a mathematical proof or anything but hear me out.
Say we start with 0.9 or 9x10^-1
Then we add 9x10^-2 to get 0.99
And so on infinitely until you get 0.999....

If we put these points on a graph, we can see that our number gets closer to 1 each time we add another 9x10^-n
In fact, every time we add another 9, the difference between 1 and our number decreases expressed by 1x10^-n
When n is infinity, the number is infinitely close to 1, and the difference between 1 and the number is infinitely small i.e. 0
Therefore 0.999... = 1

>>	Anonymous Sat Mar 28 00:20:15 2020 No.11508001 0.999...+0.000...1=1

>>	Anonymous Sat Mar 28 00:26:27 2020 No.11508009 0.9999 has oneness Aristotle eat a dick

>>	Anonymous Sat Mar 28 00:28:07 2020 No.11508015 >>11508001 Yeah but 0.999... = 1 and 0.000...1 = 0 so: 0.999... + 0.000...1 = 1 + 0 = 1 Math still checks out.

Anonymous Sat Mar 28 00:38:25 2020 No.11508034

>>11507972
I mean to divide something into perfect tenths outside of abstractly is seemingly impossible. How would you assure you have the same number of atoms or electrons. I guess you could separate ten electrons or something really small, but anything large would be hard

Anonymous Sat Mar 28 00:44:21 2020 No.11508046

0.999...

what does it mean?
0 is a number
. is a decimal indicator
9 is a number

but what does "..." mean?
continued? Repeating?

laziness, is what it is.
Not lazy for unwilling to write out more 9's. No. Rather, the laziness is the invention and loose application of what "..." is meant to define.
Laziness in failing to analyze the meta differences between fractional and decimal notation. Laziness in failing to analyze the meta act of what it means to try solving a maths problem.

1/3 != 0.3
1/3 != 0.33
1/3 != 0.333
1/3 != 0.3333
as you continue the steps towards attempted solution, it becomes clear that the repeating number you're writing doesn't even equal the fractional division.
And that raises a question of how many significant digits in the decimal do you actually need to simply settle for "close enough"?

Well, /sci/?
How many decimal digits of accuracy are required before we can just say it's close enough and apply rounding to the final digit?
15? 30? 60?

>>	Anonymous Sat Mar 28 00:48:09 2020 No.11508054 >>11508046 >how many significant digits in the decimal do you actually need no finite is enough --> infinite

>>	Anonymous Sat Mar 28 00:51:28 2020 No.11508057 File: 4 KB, 256x242, Untitled.jpg [View same] [iqdb] [saucenao] [google] You mad, broham?

>>	Anonymous Sat Mar 28 00:54:45 2020 No.11508064 >>11508054 infinite is far too much. You can't even work with it or calculate it. It's too big for your tiny pea sizes brain to comprehend.

>>	Anonymous Sat Mar 28 00:57:46 2020 No.11508068 File: 144 KB, 1024x762, 1584671966812.jpg [View same] [iqdb] [saucenao] [google] >>11507816 Not this fucking thread again.

>>	Anonymous Sat Mar 28 01:00:29 2020 No.11508073 >>11508064 >You can't even work with it 1/inf=0, no problem

Anonymous Sat Mar 28 01:00:41 2020 No.11508075

There are infinitely many numbers between a and b, where a =/= b.

Because you can "define" one number, and it is also countably singular (.00...1), .999... and 1 must not be different numbers since the set of numbers containing only {.00...1} is not infinitely large.

.999... =/= 1 is an illusion.

>>	Anonymous Sat Mar 28 01:02:46 2020 No.11508082 >>11508073 1/magical chinese dragon = 0 too, whats your point? Do you find value in asking how many times a non-number goes into 1? ... do you take brain medecine?

>>	Anonymous Sat Mar 28 01:04:47 2020 No.11508089 >>11508082 https://www.wolframalpha.com/input/?i=1%2Finf show your reference

Anonymous Sat Mar 28 01:05:39 2020 No.11508092

>>11508075
"0.999... = 1" is functionally the same as saying "0.999... doesn't even exist"

You can't prove that 0.999... doesn't exist, and I'm unfalsifiable in my justification because infinity itself is unproveable, and my attribution of 0.999... hinges on infinity.

You must submit.

>>	Anonymous Sat Mar 28 01:07:51 2020 No.11508094 >>11508092 >"0.999... = 1" is functionally the same as saying "0.999... doesn't even exist" nope 0.9... exists, and is as large as 1

>>	Anonymous Sat Mar 28 01:09:53 2020 No.11508098 Just as [math]\frac{1}{3}[/math] doesn't have a direction translation in decimal, neither does [math]0.\overline{999}[/math] have a direct translation into fractional. Decimal != Fractional English != German 0.999... != 1

>>	Anonymous Sat Mar 28 01:11:16 2020 No.11508100 >>11508098 >English != German >0.999... != 1 ooooooooh science >kek these idiots are hilarious

Anonymous Sat Mar 28 01:13:33 2020 No.11508103

>>11508094
Numbers are unique you double retard. X=Y only when X and Y are the same goddamn number.

0.9 != 1
0.99 != 1
0.999 != 1
0.9999 != 1
...
0.999... != 1

It onpy gets to equal 1 if you round on the last digit, which necessarily requires a last digit, which means you're treating infinite as finite.

>>	Anonymous Sat Mar 28 01:18:12 2020 No.11508113 >>11508103 >X=Y only when X and Y are the same goddamn number well we're in luck then >0.9999 != 1 >... >0.999... != 1 nope, finite isn't infinite duh

>>	Anonymous Sat Mar 28 01:19:13 2020 No.11508114 >>11508103 >you're treating infinite as finite. classic projection

Anonymous Sat Mar 28 01:22:23 2020 No.11508117 [DELETED]

[math]\sum_{n=1}^{\infty} \frac{9}{10^n} = [ \frac{9}{10^1} + \frac{9}{10^2} + frac{9}{10^3} + .... + \frac{9}{10^{\infty}} ] = [ \frac{9}{10} + \frac{9}{100} + \frac{9}{1000} + ... + \frac{9}{\infty} ] = [ 0.9 + 0.09 + 0.009 + ... + 0] = 0.\overline{999}0 \neq 1.\overline{000} [/math]

>>	Anonymous Sat Mar 28 01:24:40 2020 No.11508123 File: 59 KB, 960x960, 1538640230591.jpg [View same] [iqdb] [saucenao] [google] >>11508113 infinite doesn't mean what you think it means, bozo.

Anonymous Sat Mar 28 01:26:20 2020 No.11508127

[math]\sum_{n=1}^{\infty} \frac{9}{10^n} = [ \frac{9}{10^1} + \frac{9}{10^2} + \frac{9}{10^3} + .... + \frac{9}{10^{\infty}} ] = [ \frac{9}{10} + \frac{9}{100} + \frac{9}{1000} + ... + \frac{9}{\infty} ] = [ 0.9 + 0.09 + 0.009 + ... + 0] = 0.\overline{999}0 \neq 1.\overline{000} [/math]

>>	Anonymous Sat Mar 28 01:27:17 2020 No.11508130 >>11508123 I agree with WA https://www.wolframalpha.com/input/?i=infinity An unbounded quantity that is greater than every real number.

>>	Anonymous Sat Mar 28 01:27:33 2020 No.11508131 >>11508127 no

Anonymous Sat Mar 28 01:30:23 2020 No.11508140

[math] \displaystyle
\boxed{0 < p < 1} \\
p^n-1 = (p-1)(p^{n-1}+p^{n-2}+ \dots +p+1) \\
\dfrac{p^n-1}{p-1} = \sum \limits_{j=0}^{n-1}p^j \\
\displaystyle
\lim_{n \to \infty} \dfrac{p^n-1}{p-1} = \lim_{n \to \infty} \sum \limits_{j=0}^{n-1}p^j \\
\displaystyle
\dfrac{0-1}{p-1} = \sum \limits_{j=0}^{\infty}p^j \implies \dfrac{1}{1-p} = \sum \limits_{j=0}^{\infty}p^j
[/math]

[math] \displaystyle
p=0.1 \\
\dfrac{1}{1-0.1}=\frac{10}{9} = 1 + \frac{1}{9} \\
\sum_{j=0}^\infty 0.1^j= 1 + \sum_{j=1}^\infty 0.1^j \\
9+1=9+9\sum_{j=1}^\infty 0.1^j \\
1=9\sum_{j=1}^\infty 0.1^j \\
\dfrac{1}{3} = 3 \sum_{j=1}^ \infty 0.1^j = 0.333...
[/math]

Anonymous Sat Mar 28 01:32:03 2020 No.11508141

>>11508046
0.999... means [math] \lim_{n \to \infty} \sum_{i=1}^{n} \frac{9}{10^i} [/math]. This is calculus 1, dude. There's no "meta differences between fractional and decimal notation". [math] \frac{1}{3} = \lim_{n \to \infty} \sum_{i=1}^{n} \frac{3}{10^i} [/math] 0.333... and 0.999... are just shorthands because writing all of that is a pain in the ass.

>>	Anonymous Sat Mar 28 01:34:56 2020 No.11508144 1/9 = 0.111... 2/9 = 0.222... 3/9 = 0.333... 4/9 = 0.444... 5/9 = 0.555... 6/9 = 0.666... 7/9 = 0.777... 8/9 = 0.888... 9/9 = [0.999...] 1

Anonymous Sat Mar 28 01:37:06 2020 No.11508148

>>11508130
do you know what the individual words in that definition mean?
Do you know what "quantity" means?
>quantity
https://www.wolframalpha.com/input/?i=Quantity
>>how much there is or how many there are of something that you can quantify.
>quantify
https://www.wolframalpha.com/input/?i=Quantify
>>express as a number or measure or quantity

Is infinity a number?
https://www.wolframalpha.com/input/?i=Is+infinity+a+number%3F
>∞ is not a number

So what was "infinity" again?
An unbounded quantity greater than any other number?
Yet, infinity is unquantifiable, and it isn't a number.

The only infinite thing here is your loop of retardation.

>>	Anonymous Sat Mar 28 01:40:05 2020 No.11508153 >>11508148 >what "quantity" means not "magic dragon" that's for sure this case it means that the word "big" has a mathematical meaning r<inf, where r is in R

>>	Anonymous Sat Mar 28 01:41:09 2020 No.11508155 >>11508148 >other number "other"? stop pulling shit out of your ass

>>	Anonymous Sat Mar 28 01:42:32 2020 No.11508156 >>11508148 >unquantifiable nope it's a quantity

>>	Anonymous Sat Mar 28 01:49:25 2020 No.11508168 File: 1 KB, 100x100, B5882EC7-CB0F-4A48-B26C-3208AB9187FE.png [View same] [iqdb] [saucenao] [google] .99999999999 = 1-infinity^-1

Anonymous Sat Mar 28 01:49:57 2020 No.11508171

>>11508141
[math]\sum_{n=1}^{\infty} \frac{3}{10^n} = 0.\overline{333}[/math], this is a true statement, sure.
However the number value of [math]\frac{1}{3}[/math] is greater than than it.

>there is no meta differences
retard. 0.333... is neither a whole or easily rendered representation of [math]\frac{1}{3}[/math]. The fraction is simple as. The decimal "translation" of that fraction can't settle on a final solveable step denoting equality. There are clear differences, no less than when converting from one base to another.
>doesn't exist
gimme a break brainlet.

>>	Anonymous Sat Mar 28 01:51:13 2020 No.11508174 >>11508171 >value of 1/3 is greater than than it. nope >>11508140

>>	Anonymous Sat Mar 28 01:53:11 2020 No.11508178 File: 13 KB, 300x241, RoXKNzi.jpg [View same] [iqdb] [saucenao] [google] >>11508155 >what the fuck does "other" mean, damn this guy is smart with his big words n shit embarrassing

>>	Anonymous Sat Mar 28 01:55:06 2020 No.11508180 >>11508156 Quantity = number infinity is not a number that means it cannot represent a quantity and is therefore unquantifiable. Its all right there on wolframalpha, your holy book of truth.

>>	Anonymous Sat Mar 28 01:56:09 2020 No.11508183 >>11508178 "other" isn't in the definition >>11508130 "other" implies that inf is a number. inf isn't a number, that's why the definition calls it a quantity

>>	Anonymous Sat Mar 28 01:57:46 2020 No.11508185 >>11508180 >Quantity = number nope 3-3=0 inf-inf=undefined

>>	Anonymous Sat Mar 28 01:58:51 2020 No.11508187 >>11508180 >right there on wolframalpha "An unbounded quantity " it sure is

Anonymous Sat Mar 28 02:03:35 2020 No.11508196

>>11508183
I see you're tripping on words for no reason. Feel free to read the post of definitions again, then supplant wolframs actual definition with what i said about it.

Nothing changes.
>unbounded quantity greater than any real number
>DEFINE quanity: quantify
>DEFINE quantify: numbers
>IS INFINITY A NUMBER?: no
making infinity unquantifiable and wolfram's definition of infinity complete made-up nonsense.
The real kick in the nuts for you is why wolfram wouldn't just say infinity IS a number. Would make the case for it's usage a little more sensible, wouldn't it?
Why is 1/inf = 0 if infinity isn't a number?
That must mean 1/(anything that isn't a number) = 0, so 1/magical chinese dragon = 0 too.

>>	Anonymous Sat Mar 28 02:03:54 2020 No.11508198 >>11508103 can you please read up the definition of the real numbers, your issue isnt with .9999... it's with the entire system of numbers we call the "real numbers"

>>	Anonymous Sat Mar 28 02:06:42 2020 No.11508202 >>11507816 easy function Equals(a, b) => { return Abs(b - a) < Max(0.000001f * Max(Abs(a), Abs(b)), epsilon * 8) } Equals(1, 0.999999f) => true checkmate mathlets

>>	Anonymous Sat Mar 28 02:07:39 2020 No.11508203 >>11508196 >Why is 1/inf = 0 if infinity isn't a number? because if 1/inf>0, inf would somehow be bounded

>>	Anonymous Sat Mar 28 02:09:24 2020 No.11508204 >>11508196 >The real kick in the nuts for you is why wolfram wouldn't just say infinity IS a number. inf isn't a number, so no problemo

>>	Anonymous Sat Mar 28 02:10:34 2020 No.11508207 >>11508196 >you're tripping on words for no reason you're inserting new words for no good reason

Anonymous Sat Mar 28 02:11:28 2020 No.11508210

>>11508198
[math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] is a real number. Just as [math]\frac{1}{3}[/math] is a real number.

The former is a clean string of unambiguous 9's with no wiggle room towards producing a non-9 number in it's continued expansion. So why can't you accept that 0.999... exists as a real number?

>>	Anonymous Sat Mar 28 02:14:58 2020 No.11508213 >>11508210 who are you talking to?

>>	Anonymous Sat Mar 28 02:16:38 2020 No.11508215 >>11508210 .9999.... is an equivalence class of cauchy sequences, which is the definition of a real number. 1 is also an element of that same equivalence class.

>>	Anonymous Sat Mar 28 02:17:29 2020 No.11508218 >>11508213 lrn2read

Anonymous Sat Mar 28 02:21:49 2020 No.11508224

>>11508215
equivalence classes are defined by convergence. If one cauchy sequence converges to another those cauchy sequences are said to be equivalent. Whether you believe that two numbers can be equal if they are not the same is irrelevant, they have been defined to be the same. So .9999... != 1 fags really have an issue with the actual definition of equality in the real numbers.

Anonymous Sat Mar 28 02:23:55 2020 No.11508226

Pi doesn't exist. That's impressive.
I didn't know that, but it must be true.
The true, real value of pi has merely been predicted and labelled on the numberline as [math]\pi[/math], and for all the 50 trillion digits that have been discovered so far, there is still even more to discover.
But
Pi > 3
Pi > 3.1
Pi > 3.14
Pi > 3.141
Pi > 3.1415
Pi > 3.14159
its crazy. We know pi must exist on the numberline, yet we can't actually touch it. We reach out but never grasp it, always just settling with using some comprehendable handful of digits and calling that "close enough".

So if its okay to say
>3.14159265359 = pi
its easy to understand why we also say
>0.99999999999 = 1

It's cause we're all mentally retarded.

>>	Anonymous Sat Mar 28 02:26:08 2020 No.11508231 >>11508226 in base pi, pi is "10"

>>	Anonymous Sat Mar 28 02:26:14 2020 No.11508232 >>11508215 Equivalence isn't equality. 1/3 is equivalent to 0.333..., but not equal. Equivalent is approximate.

>>	Anonymous Sat Mar 28 02:29:14 2020 No.11508235 >>11508232 >Equivalence isn't equality. [citation needed]

Anonymous Sat Mar 28 02:36:39 2020 No.11508247

>>11508235
Heres a good laugh at definitions and usages
https://www.dictionary.com/browse/equivalent

one of note is what it says for math
>(of two sets) able to be placed in one-to-one correspondence.
so imagine two sets of numbers and each set has the same length
>A: [ 1 . 0 0 0 0 0 0 0 0 ... ]
>B: [ 0 . 9 9 9 9 9 9 9 9 ... ]
wheres the one-to-one equivalency beteeen A and B? they're different for every element.

>>	Anonymous Sat Mar 28 02:44:33 2020 No.11508259 If 0.999... = 1.000... then 0.999... × V = 999... 1.000... × V = 1000... 999... = 1000... if numbers get too small that we can safely ignore their differences, then too numbers must also get so big that we can safely ignore their differences.

>>	Anonymous Sat Mar 28 02:51:26 2020 No.11508272 >>11508247 >hahaha im soo smart start your own WA then wise guy >fuck these rando retards

>>	Anonymous Sat Mar 28 02:53:30 2020 No.11508274 >>11508247 oh no 500/1000 isn't 1/2 see the digits look different.... seriously, do you piss in your cereal?

>>	Anonymous Sat Mar 28 02:59:26 2020 No.11508280 >>11508274 At least i eat cereal with mine. Seems you can't help but just piss right into your own mouth and all over your face however.

>>	Anonymous Sat Mar 28 03:02:48 2020 No.11508287 >>11508280 >i have no argument

Anonymous Sat Mar 28 03:40:25 2020 No.11508338

The largest number is 1,000.
Describing larger numbers hinges on 1,000 being established.
You might think a million is a big number, but check again
>1,000,000
thats just 1,000 with 3 more zeros
Alternatively, its 1 with 6 zeros, or 7 digits.
7 is a small fraction of 1,000.
this goes on for a while.
What would you call 1,000 with 1,000 zeros after it?
"Too big, impossible" is what you'd first say. You'd be right.
but then its just [1,000]×10^[1,000],
And whats the smallest number?
Thats easy.
It's 1/(10^50)
Why?
I'll show you why.
It's 1,000 with 47 zeros after it.
It's 1,000^(16 + (2/3))
Its 50 digits long.
Nigga can you even do math with 50 digits?
No. You do finger math, 1 digit. You'll grab a pen and paper and do like 3 digit math.
You'll use your casio calculator and do 8 digit math. That shit is accurate enough to put niggas on the moon. 8 digits. Think about it.

You learn how to program computer and you'll get 15 digit math. They do flybys with pluto on 15 digit math, nigga. Think about it.

So whats special about 50 digits?
nigga, map(8,15 -> moon,pluto)
(8) Moon: 2.4 × 10^5 miles
(15) Pluto: 2.6 × 10^9 miles
(50) = 2.8 × 10^24 miles
size of the universe is 5.5 × 10^23 miles

16 + (2/3) = 16.6666...
guess what that is, nigga.
16.6666... milliseconds × 60 = 1 second
60 minutes in an hour
60 seconds in a minute
60 (16 + (2/3))milliseconds in a second.
60 + 60 + 60 = 180°, half a circle
Whats half a circle?
[math]\pi[/math].
Think about it.

>>	Anonymous Sat Mar 28 03:56:17 2020 No.11508356 >>11508338 the pills won't help if you don't actually take them

>>	Anonymous Sat Mar 28 04:01:09 2020 No.11508361 >>11508356 bozo who believes in infinity trying to give advice to anyone else. [math] L M A O [/math]

>>	Anonymous Sat Mar 28 04:06:45 2020 No.11508370 >>11508171 based

>>	Anonymous Sat Mar 28 04:18:53 2020 No.11508389 >>11507839 what makes you think 9 times 0.99999... is 9?

>>	Anonymous Sat Mar 28 04:19:11 2020 No.11508390 >>11508361 >i have no argument

>>	Anonymous Sat Mar 28 04:20:18 2020 No.11508394 >>11508370 >than than based >every retard ever

>>	Anonymous Sat Mar 28 04:21:22 2020 No.11508396 >>11508389 >what makes you think i think 9 times 0.99999... is 9?

>>	Anonymous Sat Mar 28 04:22:13 2020 No.11508398 >>11507816 Well some mathematical systems do allow infinitesimals

>>	Anonymous Sat Mar 28 04:22:27 2020 No.11508399 >>11508389 what makes you think i think 9 times 0.99999... is 9?

>>	Anonymous Sat Mar 28 04:32:21 2020 No.11508411 File: 182 KB, 953x613, .9 Repeating = 1.jpg [View same] [iqdb] [saucenao] [google] >>11507894 >>11507916 >>11508001 >>11508015 >>11508046 >>11508064 >>11508098 >>11508103 >>11508127 >>11508171 >>11508259

>>	Anonymous Sat Mar 28 04:35:13 2020 No.11508414 >>11508411 tldr can you remake this image in the form of a wojak comic so i can understand it

>>	Anonymous Sat Mar 28 04:37:01 2020 No.11508416 >>11508414 >can you remake this image no

>>	Anonymous Sat Mar 28 04:46:59 2020 No.11508425 >>11508414 No.

Anonymous Sat Mar 28 04:53:34 2020 No.11508435

"0.999..." means [math]\sum_{n=1}\frac{9}{10^n}[/math]
Thats what "0.999..." means.
It doesn't mean it has infinite 9's, it just means that any measure will have as many finite 9's as you're willing to deal with for any given required application. As many as you want for which you can calculate with. You can't "have them all" because you can't calculate with infinite digits, the work would never end, and you'd never get a result.

Moreover, "0.999..." is NOT the result you get when you equate 1/3 into decimal and multiply it by 3.
That repeating 9 number you get in that case is strictly an error in the way we look at the math. As in, we expect an answer to be solved, and find it hard to understand that an answer provided from attempting to solve would actually be unsolved.
It's not
>1/3 = 0.333...
>3(1/3) = 3(0.333...)
>3/3 = 0.999...

It's
>1/3 > 0.333...
>3(1/3) > 3(0.333...)
>3/3 > 0.999...

There is no ambiguity that [math]\frac{n}{n}[/math]=1, however not all [math]\frac{n}{k}[/math] have direct translations from fractional to decimal.
[math]\frac{1}{2} > \frac{1}{3} > \frac{1}{4} \frac{1}{5} > \frac{1}{6} > \frac{1}{7} > \frac{1}{8} > \frac{1}{9}[/math]
[math]0.5 > x > 0.25 > 0.2 > x > x > 0.125 > x[/math]
the x's are decimal values that have no direct translation from their fraction counterpart.

With that established, it must be understood that any observation or usage of an instantiated repeating number, such as:
>x = 0.999...
must also convey information about the finite degree of accuracy desired to work with it.
>x = 0.9999999999
for example
and now we can do math with it
>10x = 9.9999999990
>10x-x = 8.9999999991
>9x = 8.9999999991
>x = 0.9999999999

remember infinity is not a number.

>>	Anonymous Sat Mar 28 04:56:31 2020 No.11508439 >>11508411 You're really proud of this image and constantly repost it in every thread despite every single thing it's claiming is false.

Anonymous Sat Mar 28 04:59:03 2020 No.11508443
File: 3.00 MB, 1280x9474, 1554337018090.jpg [View same] [iqdb] [saucenao] [google]

>>11507816
The inability many people today who view themselves as being "scientific" as well as math fans (left-brain prisoners) have in comprehending that .999 isn't the same as 1, is completely connected to their inability to grasp eternity and infinity. Their minds have basically been programmed to believe eternity and infinity are impossibilites. Over the course of the last 10 or so centuries of indoctrination into an alien world-view, they've "learned" to be unable to comprehend it.

This difficulty they have with eternity/infinity shows up in many different fields, from math to astrophysics.

This mental handicap is inherited directly from the (((Abrahamic))) religions, more specifically Christinsanity for us Westernerns. In it's origin, the inability to understand infinity and eternity is 100% Judaic in thought/philosophy. In contrast, the non-Jewish man; the Pagan man, at least the /European/ Pagan man, never had any problem with infinity and eternity. Christinsanity introduced into the minds of people the idea of life and the world/universe being linear, starting from point A and ending with a point B, whereas in the Native European world-view everything is infinite, a circle.

That's why many people today can't understand that .999 repeating forever will never reach 1 -- they refuse to accept the idea of an infinite/eternal repetition. Saying "it's 1" is their method of escaping from the uncomfortable (and to them insurmountable) challenge which the concept of infinity/eternity is to thier Judaically-induced mental disease.

>>	Anonymous Sat Mar 28 04:59:06 2020 No.11508444 >>11508411 Autism

>>	Anonymous Sat Mar 28 05:00:16 2020 No.11508448 >>11508439 I’m going to make an image to counter it

>>	Anonymous Sat Mar 28 05:10:07 2020 No.11508461 >>11508443 No, infinity and eternity exist, it just has nothing to do with numbers. That was a big wall of text for nothing.

>>	Anonymous Sat Mar 28 05:13:19 2020 No.11508462 >>11507816 there are two options: either 1 - 0.999... = 0 or 1 - 0.999... > 0 the second option results in contradictions. therefore it's the first option which is true. QED

>>	Anonymous Sat Mar 28 05:15:24 2020 No.11508466 File: 468 KB, 420x420, 55276badb4dd080a5be872d5f8617bbb.png [View same] [iqdb] [saucenao] [google] >>11508462 >1 minus a number smaller than 1 is greater than 0 >this is a contradiction

>>	Anonymous Sat Mar 28 05:16:04 2020 No.11508468 >>11508461 Congratulations, your mind isn't entirely Jewish.

>>	Anonymous Sat Mar 28 05:17:19 2020 No.11508469 >>11508466 >0.999... is smaller than 1 prove it

>>	Anonymous Sat Mar 28 05:20:16 2020 No.11508472 >>11508469 1 > 0.9

>>	Anonymous Sat Mar 28 05:20:52 2020 No.11508474 >>11508472 true and irrelevant

Anonymous Sat Mar 28 05:25:54 2020 No.11508482

>>11508474
1 > 0.9000000000000000000...
1 > 0.9900000000000000000...
1 > 0.9990000000000000000...
1 > 0.9999000000000000000...
1 > 0.9999900000000000000...
1 > 0.9999990000000000000...
1 > 0.9999999000000000000...
1 > 0.9999999900000000000...
1 > 0.9999999990000000000...
do you see a repeating pattern forming here and can you imagine what it would continue to look like?
...
1 > 0.9999999999999999999...
1 > 0.999...

thats just how it do.
thats just how it be.
simple as.
intuitive.

>>	Anonymous Sat Mar 28 05:27:40 2020 No.11508483 >>11508461 >nothing to do there is a defined relation >>11508130 >>11508153

>>	Anonymous Sat Mar 28 05:28:22 2020 No.11508485 >>11508439 >Pouring one bottle of water into three cups, then back into one, results in less than one cup >false statement Fucking weapons-grade retardation

>>	Anonymous Sat Mar 28 05:29:37 2020 No.11508488 2 real numbers are equal if there is no rational number between them, by the dedekind cuts definition (a real number is equal to the set of rational numbers smaller than it). There is no rational number between 0.999.... and 1. Hence 0.9999...=1

Anonymous Sat Mar 28 05:29:40 2020 No.11508489

>>11508435

If we use base 9 for the 1/3 argument:

>1/3 = 0.3
>2/3 = 0.6
>3/3 = 1

Or if we use base 6:

>1/3 = 0.2
>2/3 = 0.4
>3/3 = 1

Or base 3:

>1/3 = 0.1
>2/3 = 0.2
>3/3 = 1

Then we can see the 0.9999 shit is only caused by our base 10 decimal system.

>>	Anonymous Sat Mar 28 05:29:53 2020 No.11508491 >>11508482 >zero repeating is same as 9 repeating lol no total retard

>>	Anonymous Sat Mar 28 05:30:00 2020 No.11508492 File: 277 KB, 585x606, 1585113630285.png [View same] [iqdb] [saucenao] [google] >>11508483 wow retard. >>11508148

>>	Anonymous Sat Mar 28 05:30:20 2020 No.11508493 >>11508482 1 > 0.99....9 for any finite string of 9's only implies 1 ≥ 0.999... but this is a common beginner mistake, don't worry about it

>>	Anonymous Sat Mar 28 05:32:20 2020 No.11508496 >>11508492 cool argument bro >>11508148 so?

>>	Anonymous Sat Mar 28 05:32:20 2020 No.11508497 >>11508482 0.99>0.9 0.999>0.99 0.9999>0.999 0.99999>0.9999 0.999999>0.99999 do you see a repeating pattern forming here and can you imagine what it would continue to look like? .... 0.999...>0.999...

>>	Anonymous Sat Mar 28 05:33:23 2020 No.11508499 >>11508497 kek

>>	Anonymous Sat Mar 28 05:34:25 2020 No.11508502 >>11508493 >>11508140

>>	Anonymous Sat Mar 28 05:34:43 2020 No.11508503 >>11508482 0.999... > 0.9 0.999... > 0.99 0.999... > 0.999 0.999... > 0.9999 0.999... > 0.99999 do you see a repeating pattern forming here and can you imagine what it would continue to look like? ... 0.999... > 0.999... M I N D B L O W N

>>	Anonymous Sat Mar 28 05:40:06 2020 No.11508513 >>11508488 [math]sum_{n=1}^{\infty} \frac{9}{10^n} = 0.\overline{999}_9 < \sum_{n=1}^{\infty} \frac{10}{11^n} < \sum_{n=1}^{\infty} \frac{11}{12^n} < \sum ... < 1.0[/math] learn how to do math.

>>	Anonymous Sat Mar 28 05:42:16 2020 No.11508517 >>11508513 that looks like a zodiac killer letter try real math sometimes

>>	Anonymous Sat Mar 28 05:43:09 2020 No.11508518 >>11508503 I mean you're not wrong, if both sides grew at the same rate then there were always more 9's on the left side number. Oh wait, do you think infinite is finite?

>>	Anonymous Sat Mar 28 05:46:30 2020 No.11508529 >>11508518 >both sides grew left hand side remains constant

>>	Anonymous Sat Mar 28 05:47:44 2020 No.11508531 >>11508513 another reminder that [math]a_n < K[/math] doesn't imply [math]\sup_{n \in \mathbb{N}}\{a_n\} < K[/math]

>>	Anonymous Sat Mar 28 05:48:09 2020 No.11508532 >>11508503 >>11508497 >these mentally retarded niggers whose mothers' drank bleach while pregnant literally think infinity is a process that ends

Anonymous Sat Mar 28 05:49:15 2020 No.11508534

A sequence of rational numbers (q_i) is called Cauchy if:
- For any positive rational number e>0, there exists a natural number N such that for all natural numbers n,m>N, |q_n - q_m|<e.
-----------------
Real numbers ARE NOT:
- sequences of digits with a decimal point somewhere
- mystical undefined quantities that behave like magic
- infinite processes (whatever that means)

Real numbers ARE:
- Equivalence classes of Cauchy sequences of rational numbers ( sequence a_n is equivalent to b_n if the sequence (a_n -b_n) converges to 0 in the rational numbers)
- Equivalently, the set of Dedekind cuts (nonempty proper subsets of the rational numbers A such that 1) for all x in A and y<x implies y in A; 2) A does not contain a maximum
--------------------
The notation x=0.(d_1)(d_2)(d_3).... (d_i are digits) DOES NOT stand for:
- An infinite process (this term is meaningless in mathematics).
- The sequence of digits d_i
- An element of hyperreals or surreal numbers.

It DOES stand for:
- The least real number (or the least rational number, if such exists, because they are the same) that is not smaller than any of the numbers {0.d_1, 0.d_1d_2, 0.d_1d_2d_3,...}
- Equivalently, the real limit of the Cauchy sequence (0.d_1, 0.d_1d_2, 0.d_1d_2d_3,...).
- Equivalently, the equivalence class of in the Real numbers of the Cauchy sequence (0.d_1, 0.d_1d_2, 0.d_1d_2d_3,...).
- Equivalently, in the Dedekind cuts definition of the real numbers, the Dedekind cut containing all the numbers (0.d_1, 0.d_1d_2, 0.d_1d_2d_3,...) together with all the rational numbers smaller than any of its elements.

Now that we've got the definitions out of the way,
- By Dedekind cuts definition of the real numbers, two different real numbers have a rational number strictly between them.
...cont

>>	Anonymous Sat Mar 28 05:49:28 2020 No.11508535 >>11507925 If there are three apples and you take one. You have taken exactly a third of the apples.

>>	Anonymous Sat Mar 28 05:50:02 2020 No.11508537 File: 76 KB, 239x243, 1551451198820-1.png [View same] [iqdb] [saucenao] [google] >>11508529 >lets pretend infinite is finite shit nigga its like it's literally just impossible for you to win.

Anonymous Sat Mar 28 05:50:17 2020 No.11508538

>>11508534
- Same holds for the Cauchy sequence definition of the real number: if x<y are different real numbers, let the Cauchy sequences x_i and y_i represent them. Then (y_i - x_i) is a Cauchy sequence that is bounded above by some e>0. Thus there is a rational number strictly between x_i and y_i.

In conclusion, since 0.999... and 1 have no rational numbers between them, they must be equal.

>>	Anonymous Sat Mar 28 05:51:55 2020 No.11508542 >>11508537 >I have no argument

>>	Anonymous Sat Mar 28 05:52:16 2020 No.11508543 >>11508535 alright billybob, now convert those apples into a fraction and convert that fraction into a decimal. Technically you have to stop at the fraction for final equality since the decimal suffers translation error.

>>	Anonymous Sat Mar 28 05:54:03 2020 No.11508547 >>11508542 Who are you quoting?

>>	Anonymous Sat Mar 28 05:54:34 2020 No.11508548 >>11508535 imagine the smell

>>	Anonymous Sat Mar 28 05:55:19 2020 No.11508550 >>11508287 >>11508390 >>11508542 oh you're quoting yourself.

>>	Anonymous Sat Mar 28 05:55:53 2020 No.11508552 >>11508543 0.1, in base 3

>>	Anonymous Sat Mar 28 05:56:11 2020 No.11508553 >>11508547 you

>>	Anonymous Sat Mar 28 05:56:42 2020 No.11508554 >>11508144 ^underrated

>>	Anonymous Sat Mar 28 05:56:57 2020 No.11508555 >>11508552 decimal is base 10. why are you talking about trinary.

>>	Anonymous Sat Mar 28 06:04:14 2020 No.11508563 >>11508532 >I don't know what a supremum or a limit is

>>	Anonymous Sat Mar 28 06:11:35 2020 No.11508574 imagine teeter tottering between thinking infinity is either A or B, when in reality it's C and you're nowhere close.

>>	Anonymous Sat Mar 28 06:12:31 2020 No.11508575 >>11508555 what's holy about base 10 1/2 is 0.333... in base 7 does that mean 0.5 doesn't exist?

>>	Anonymous Sat Mar 28 06:19:25 2020 No.11508585 >>11508555 0.1 in base 3 = 0.333... in base 10 The base doesn’t matter

>>	Anonymous Sat Mar 28 06:28:38 2020 No.11508596 >>11508585 >0.1 in base 3 = 0.333... in base 10 >= wrong. no equality. 0.1[END] in base-3. 0.[math]33333[/math]33333[math]_{3333...}[/math] endlessly in base-10. no final mantissa means no final solution means no direct equality.

>>	Anonymous Sat Mar 28 06:29:32 2020 No.11508599 >>11508596 >>11508575

>>	Anonymous Sat Mar 28 06:57:03 2020 No.11508632 >>11508554 tl;dr 1/9 = 0.111... + 8/9 = 0.888... = 9/9 = 0.999...

Anonymous Sat Mar 28 07:20:46 2020 No.11508677

>>11508632
a fraction or identity which, when rendered as a decimal containing repeating sequences, holds that the value of the fraction or identity is greater than the decimal rendering.
1/9 != 0.1111...
1/9 > 0.111...
8/9 > 0.888...
9/9 > 0.999...
repeating decimals like these, in relation to fractions like these, have a different component of truthfulness to them than a decimal with a last digit, like 1/2 = 0.5

(9/9 = 0.999...) is a false statement. The fraction equate to 1, and the decimal is in error (not in rendering, but in comparison to what it's being rendered from), relative to the truth component being "="
However
(9/9 > 0.999...) is a more truthful statement. The fraction equates to 1, and 1 is larger than some 0.9 number, relative to the comparison ">"

And even though the latter is "more truthful", it still is not entirely truthful, because "0.999..." can represent infinitely many different values in the spectrum of [math]\lim_{k\rightarrow \infty} \sum_{n=1}^{\infty} \frac{k}{(k+1)^n}[/math], which itself is an allowable inconvenience because [math]\infty[/math] wasn't ejected out of mathematics with hearty laughs the moment it was introduced like it should have been, leading to the modern day where "..." is used to hide or otherwise ignore unique identifiers in long numbers that are too inconveniently long to write out.

>>	Anonymous Sat Mar 28 07:22:59 2020 No.11508679 >>11508677 wall-of-text schizo

>>	Anonymous Sat Mar 28 07:35:55 2020 No.11508712 >>11508679 infinite is infinite, and you don't have the capacity to deal with it.

Anonymous Sat Mar 28 07:42:47 2020 No.11508723

threadly reminder that
[eqn]0 \leq 1 - 0.999\dots \leq \tfrac{1}{10^n}[/eqn]
holds for every [math]n[/math]. unless you can prove that there exist non-zero non-negative numbers which are smaller than [math]\tfrac{1}{10^n}[/math] for all [math]n[/math], this implies
[eqn]1 - 0.999\dots = 0[/eqn]

>>	Anonymous Sat Mar 28 07:57:57 2020 No.11508744 >>11508712 >deal with it it's big, so 1/inf=0

>>	Anonymous Sat Mar 28 08:12:05 2020 No.11508764 >>11508723 >my statement is correct unless you can prove otherwise. Anon, that's not how proofs work.

>>	Anonymous Sat Mar 28 08:13:28 2020 No.11508766 >>11508764 >i can't find the error m-muh feelings

>>	Anonymous Sat Mar 28 08:19:47 2020 No.11508774 >>11508764 it's not supposed to be proof, it's an attempt to lure schizos into trying to prove something which is false

Anonymous Sat Mar 28 08:23:03 2020 No.11508780
File: 10 KB, 618x175, Slope Proof .999...≠ 1.png [View same] [iqdb] [saucenao] [google]

What is the slope of line BZ?
How is it different from line BW?

Note that if you try to claim that line ZW is meaningless or doesn't exist somehow, then neither does .999...

>>	Anonymous Sat Mar 28 08:25:43 2020 No.11508787 >>11508780 pic "proofs" aren't proofs can draw another "proof" that shows the opposite in both cases it's just a nice analogy, nothing more

>>	Anonymous Sat Mar 28 08:28:39 2020 No.11508794 >>11508787 >can draw another "proof" that shows the opposite No you can't. Try it. Or better still, answer the question instead of trying to "disqualify" it.

Anonymous Sat Mar 28 08:33:44 2020 No.11508802 [DELETED]

>>11508794
https://i.imgur.com/BKxlscC.png
As long as the distance AB>0, C moves along the bottom horizontal line.
Once AB=0, C is on the top horizontal line, if anywhere.
This is infinity. Infinity is larger than any real number. Infinity isn't a number.

>inb4 assuming circles exist
>thinks continuity is important here

>inb4 assuming infinite lines exist
if you think a line can't be longer than M,
it still stands that an M length BC line
reaches less to the right, than an M-long horizontal line along the top horizontal

Anonymous Sat Mar 28 08:34:11 2020 No.11508803

>>11508780
Did you just try to appeal to intuition by assigning infinity to a distinct point in a geometric illustration? As far as that can charitably be said to make sense at all, the slope of line BZ is 0, the proof of witch would be essentially the same proof by limits as proving 1=0.999...

>>	Anonymous Sat Mar 28 08:34:20 2020 No.11508804 >>11508787 >pic "proofs" aren't proofs It is apparent that OP has not even a high-school level understanding of math. So what other means do you think are available to prove something to him?

Anonymous Sat Mar 28 08:34:48 2020 No.11508806

>>11508794
https://i.imgur.com/BKxlscC.png
As long as the distance AB>0, C moves along the bottom horizontal line.
Once AB=0, C is on the top horizontal line, if anywhere.
This is infinity. Infinity is larger than any real number. Infinity isn't a number.

>inb4 assuming circles exist
thinks continuity is important here

>inb4 assuming infinite lines exist
if you think a line can't be longer than M,
it still stands that an M length BC line
reaches less to the right, than an M-long horizontal line along the top horizontal

>>	Anonymous Sat Mar 28 08:37:36 2020 No.11508811 >>11508034 yes but who cares?

>>	Anonymous Sat Mar 28 08:40:38 2020 No.11508815 >>11508596 yes because 0.333... < 1/3

>>	Anonymous Sat Mar 28 08:42:02 2020 No.11508818 >>11508804 pics assist in understanding, but that's all. They fail as a rigorous proof because just-graphics assumes distance=length, which the density-of-numbers easily breaks.

>>	Anonymous Sat Mar 28 08:43:56 2020 No.11508822 >>11508811 this guy >>11507972

>>	Anonymous Sat Mar 28 08:49:36 2020 No.11508831 >>11507839 This same logic was taught to me by a Math doctor It seems legit

Anonymous Sat Mar 28 08:50:57 2020 No.11508833

>>11508723
what you're saying is not a reasonable math function without first addressing how you're creating your 0.999.... reference.

for example:
[math]1 - \sum_{n=1}^{\infty} \frac{9}{10^n} \leq \frac{1}{10^n}[/math] might be more of what you're trying to express.

And in that case, it works out fine in proving small numbers exist.
for example when n=3
1 - 0.999 = 0.001; 1/10^3 = 1/1000 = 0.001
all checks out.

the issue of virtually all misunderstandings of this revolve explicitly around what the fuck infinity means and what the fuck "..." dot repetition means, of which neither are explained well or used correctly.

to break it down, you seem to want to treat [math]0.999\dots[./math] as if it were a finite, contained, bounded set of knowable length, of which at some arbitrary point within (or at the end of) that set, some arbitrary (unnoted) restriction arises where there can be no more continued math, such that you treat it like:
[ 0 . 9 9 9 9 9 9 9 9 . . . ]
aka, "contained" between the [ and ] brackets, leading to your math of
>[ 1 . 0 0 0 0 0 0 0 0 . . . ]
- [ 0 . 9 9 9 9 9 9 9 9 . . . ]
=[ 0 . 0 0 0 0 0 0 0 0 . . . ]
while either not realizing the problem or otherwise hoping no one else notices the problem of what information " . . . ] " is being used to hide.

if we take that infinity is unbounded, unlimited, on-going, continual, ever-lasting; then there is no identifiable unique "chunk" or sequence we can attain from within it. If we also take that the word "infinite" can be used to describe the size of "the set of all numbers", aka:
[math] \underbrace{[ 0, 1, 2, 3, 4, 5, 6, 7, \dots ]}_{size=\infty}[/math]
but this is a collection of definitely finite values 'between' [math] {1\rightarrow \infty}[/math]
which ultimate derives a definition of infinity which means any test of n as an element within an infinite set, is indeed a finite number, and always will be, continually.

Anonymous Sat Mar 28 08:55:26 2020 No.11508842

>>11508818
>pics assist in understanding, but that's all.
>They fail as a rigorous proof because just-graphics assumes distance=length
OP is nowhere near that level. His teacher has shown him a pic of an apple, a pic of a car, and a pic of a nose, and OP is supposed to know from that what "1" means to everybody. Pics of two apples, two cars and two ears prove to OP that "1" is not "2", and so on. It is not a wonder that he thinks that his equation needs "proof". Indeed, it is very much in doubt that he even knows the meaning of the symbols on the LHS.

>>	Anonymous Sat Mar 28 08:55:52 2020 No.11508844 >>11508833 >how you're creating i create them by dancing around the house in clogs now what?

>>	Anonymous Sat Mar 28 08:57:07 2020 No.11508846 >>11508844 so you're merely just pretending to do math?

>>	Anonymous Sat Mar 28 08:58:31 2020 No.11508852 >>11508846 nein nein nein...

>>	Anonymous Sat Mar 28 09:00:48 2020 No.11508857 >>11508852 >nein nein nein... Prove nein nein nein... = nazi

>>	Anonymous Sat Mar 28 09:00:55 2020 No.11508858 >>11508534 >>11508538 You are completely correct. But who says we have to be talking about the real numbers, especially given that non-archemedian systems which include infinitesimals can be rigorously defined?

Anonymous Sat Mar 28 09:01:47 2020 No.11508860

>>11508833
>to break it down, you seem to want to treat [math]0.999\dots[./math] as if it were a finite, contained, bounded set of knowable length, of which at some arbitrary point within (or at the end of) that set, some arbitrary (unnoted) restriction arises where there can be no more continued math, such that you treat it like:
Incorrect.

>if we take that infinity is unbounded, unlimited, on-going, continual, ever-lasting; then there is no identifiable unique "chunk" or sequence we can attain from within it.
Completely wrong. Since the digits repeat we know exactly what every part of the sequence is. You assume, based on nothing, that just because something is infinite in some way it cannot be operated on. There is an entire field of math that does just that, called the calculus.

>which ultimate derives a definition of infinity which means any test of n as an element within an infinite set, is indeed a finite number, and always will be, continually.
So what?

>>	Anonymous Sat Mar 28 09:03:02 2020 No.11508862 >>11508857 the clogs are dutch you dork

>>	Anonymous Sat Mar 28 09:04:26 2020 No.11508864 >>11508815 0.333 < 1/3 0.3333 < 1/3 0.333...n =/= 0.333... for any n

>>	Anonymous Sat Mar 28 09:12:52 2020 No.11508873 >>11508864 >0.333 < 1/3 >0.3333 < 1/3 yes >0.333...n =/= 0.333... for any n nope, the "..." means infinite digits n*10^-inf=0, so it's meaningless so you get 0.333...=0.333...

>>	Anonymous Sat Mar 28 09:19:27 2020 No.11508884 >>11508873 >nope, the "..." means infinite digits You just agreed with him. >n*10^-inf=0, so it's meaningless It's undefined, but that's a non sequitur anyway. >0.333...=0.333... But 0.333...3 =/= 0.333..

>>	Anonymous Sat Mar 28 09:20:16 2020 No.11508886 0.999... = 1 1-(1/infinity) = 1 -(1/infinity) = 0 1/infinity = 0 if 1/infinity = 0 then e = (1+(1/infinity))^infinity e = (1)^infinity e = 1 so 0.999... != 1

>>	Anonymous Sat Mar 28 09:21:21 2020 No.11508888 excuse me sirs, but the very first assumption is dubious. is 1/3 really equal to 0.333..? isnt 4 the last digit?

Anonymous Sat Mar 28 09:22:42 2020 No.11508892

>>11508860
calculus is explicitly finite. Any math that "deals" with "infinity" yet produces an answer in real time is always, explicitly using finite operations to do so. Fourier transforms, even the [math]\sum_{n=1}^{\infty} \text{and} \lim_{n \rightarrow \infty}[/math] functions use this shit explicitly finitely and tend to mean that their use of [math]\infty[/math] is either [math]not[/math] literal, or that their literal usage is as defined here:
>which ultimately derives a definition of infinity which means any test of n as an element within an infinite set, is indeed a finite number, and always will be, continually.
with an addendum:
>(finite to user's discretion per application)

"proving" infinity "exists" is almost as difficult as proving something that no longer exists ever existed at all. Can you "prove" the WTC twin towers exist? All you could use to "prove" it are photos and videos, but if anyone never saw the WTC twin towers for themselves, those photos and videos merely represent something that is completely out of reach of ever getting to personally see.

that aspect of "infinity" is also completely out of reach of ever personally getting to see it, account for it, measure it, etc. It's like looking out into space and saying you can see the edge of the universe as clearly as you might see an edge of a cardboard box, or the edge of a cliff hanging over a coastline facing the ocean. The truth is, you can't "see" the edge of the universe, and you certainly can't grasp it or reach it even if you could. Same goes for infinity. You can't "see" where it ends, and you certainly can't grasp it or reach it even if you could.

This is all in relation to assuming [math]0.999\dots[/math] explicitly contains infinite 9's, as if you know it as truth, as if you'd seen it yourself, as if you'd measured it and contained it conveniently in 8 text characters; and this is the false assumption leading to the issues at hand.
There are not "infinite" 9's there.

>>	Anonymous Sat Mar 28 09:24:04 2020 No.11508896 >>11508873 >the "..." means infinite digits Exactly. And "...n" means finite digits. So? >n*10^-inf=0, so it's meaningless This is completely irrelevant to anything I said.

>>	Anonymous Sat Mar 28 09:30:36 2020 No.11508906 >>11508896 >"...n" means finite digits. nope

>>	Anonymous Sat Mar 28 09:31:39 2020 No.11508909 >>11508892 >calculus is explicitly finite lol no

>>	Anonymous Sat Mar 28 09:32:52 2020 No.11508911 >>11508888 >>11508140

>>	Anonymous Sat Mar 28 09:34:37 2020 No.11508914 >>11508909 >lol no then calculus doesn't produce usable answers. but it does. so it must use infinity explicitly finitely, because doing infinite work would require infinite time, meaning no answer would ever be produced in finite time.

>>	Anonymous Sat Mar 28 09:34:52 2020 No.11508915 >>11508886 >e = (1+(1/infinity))^infinity 1^inf is undefined

Anonymous Sat Mar 28 09:35:10 2020 No.11508916

>>11508858
Well I was talking about the standard notation of course. The point is, if you're using a different number system, you should specify this. 0.9999...= 1 is a trivial theorem following from the way we define decimal expansions.
This whole thread is all about people confusing notation with the meaning behind it.
0.999... is an expression that has a standard meaning in mathematics. "0.999..." itself is not a number, it's an expression that represents a number.
The whole debate would be instantly solved if they people who claim 0.999... =/= 1 would specify what they mean by 0.999.... But they never do. They always give vague, meaningless answers about "processes" and "infinities". Nonsense really. I don't know why people still engage with these retards.

>>	Anonymous Sat Mar 28 09:36:53 2020 No.11508917 >>11508914 >then calculus doesn't produce usable answers. nope it works, and f'(x) is defined with limits

>>	Anonymous Sat Mar 28 09:40:29 2020 No.11508930 >>11508917 talking to you is like talking to a block of conjac. dear fuck your brain is nothing but jelly and you never add anything useful to these threads.

Anonymous Sat Mar 28 09:41:15 2020 No.11508931
File: 13 KB, 439x352, p1.png [View same] [iqdb] [saucenao] [google]

>>11508780
I assume that the two horizontal lines are supposed to be number lines. then Z and W aren't supposed to be drawn on the lines, because they don't represent any number. they actually represent so-called "ideal points", which are basically points on the horizon.

pic related is what you see if you draw a finite portion of your picture on a canvas and you tilt the canvas a little.

Anonymous Sat Mar 28 09:42:29 2020 No.11508933

>>11508892
>calculus is explicitly finite. Any math that "deals" with "infinity" yet produces an answer in real time is always, explicitly using finite operations to do so.
Yes, that's exactly my point.

>>which ultimately derives a definition of infinity which means any test of n as an element within an infinite set, is indeed a finite number, and always will be, continually.
You keep repeating this without explaining how it's relevant.

>"proving" infinity "exists" is almost as difficult as proving something that no longer exists ever existed at all.
There is no need to prove anything in math "exists," but if it makes you feel better, infinite decimals and infinite limits are used all over physics.

>Can you "prove" the WTC twin towers exist?
Do you understand the difference between math and empiricism? Theorems vs. Facts?

>This is all in relation to assuming 0.999… explicitly contains infinite 9's, as if you know it as truth, as if you'd seen it yourself, as if you'd measured it and contained it conveniently in 8 text characters
LOL, now you seem to think symbols have meaning beyond their definition, as if they need to be discovered in a Platonic realm. Choose a position already.

>There are not "infinite" 9's there.
Why not? You haven't actually given an argument, just wasted a bunch of electronic space. None of it is math.

>>	Anonymous Sat Mar 28 09:43:32 2020 No.11508935 >>11508906 >nope Nope.

Anonymous Sat Mar 28 09:45:21 2020 No.11508944
File: 22 KB, 419x540, p2.png [View same] [iqdb] [saucenao] [google]

>>11508780
>>11508931
pic related is what happens if you draw the whole picture with correct scale and then tilt the canvas. we can see that the points Z and W actually coincide, BZ and BW coincide, and therefore slope of BZ is 0. which proves 0.999... = 1.

>>	Anonymous Sat Mar 28 09:48:04 2020 No.11508949 >>11508935 k, have fun by yourself

Anonymous Sat Mar 28 09:48:54 2020 No.11508954

>>11508931
the graphic merely aligns with zeno's paradoxes of Achilles and the tortoise, which itself boils down to [math]\sum_{n=1}^{\infty} \frac{1}{2^n}[/math], which is also similarly applied to zeno's Arrow paradox, defining [math]\frac{1}{\infty}[/math] cannot be possible, for infinite sequential addition of the result would never produce 1.

there always exists a smallest finite part, regardless of how arbitrary it may be.

>>	Anonymous Sat Mar 28 09:50:14 2020 No.11508957 >>11508930 >like talking to a block of conjac you should know

>>	Anonymous Sat Mar 28 09:51:26 2020 No.11508958 >>11508888 It's funny how truths that have been clear since the third grade can still be legitimately called into question. Math is funny that way.

Anonymous Sat Mar 28 09:53:40 2020 No.11508964

>>11508954
No need to define 1/inf, it never occurs in the sum.

>for infinite sequential addition of the result would never produce 1.
What do you mean by never? Are you saying each addition step takes some amount of time? It doesn't, and you can solve it instantly using calculus.

>there always exists a smallest finite part, regardless of how arbitrary it may be.
Incorrect.

>>	Anonymous Sat Mar 28 09:54:36 2020 No.11508969 >>11508906 What else would it reasonably mean?

Anonymous Sat Mar 28 09:55:07 2020 No.11508972

>>11508916
Give them a break, they're generally people who have yet to be exposed to modern mathematical formalism, but feel that 0.999... potentially stands for some quantity that, *could* be infinitesimally distinct from 1, and feel that statements against this are blind attacks against this possibility. In a sense, they are right to point out that most of the proofs typically offered against this are things that implicitly assume that they are using a specific set of numbers, but without actually defining it, and showing that, for instance, the Archimedean property holds.

Given that the Dedekind construction of the reals is relatively recent, compared to Newton's intuitive use of infinitesimals, there in a sense, actual justification to the person who claims that 0.999... = 1 is debatable, in the absence of prior agreement of the conventions being used. It's one thing to explicitly claim that this is false with regard to the reals, using standard notation, but another to merely point out that the notation could be defining some sequence of numbers which converge to something which could be distinct from 1 in some hypothetical set of numbers where this might be possible, which is something that isn't generally going to be 'proven' in these kinds of debates.

>>	Anonymous Sat Mar 28 09:55:21 2020 No.11508974 >>11508954 >here always exists a smallest finite part, let's pretend finite is infinite

Anonymous Sat Mar 28 10:01:44 2020 No.11508989 [DELETED]

>>11508969
reasonably, it's a dumb ass way of writing a meaningless digit
anything after the "...", aka ellipsis indicates the previous digit repeats forever
so if you have to tack something on the right side of ..., it's either meaningless or literally infinitely small - the value of n is n*10^-inf=0

>>	Anonymous Sat Mar 28 10:04:28 2020 No.11508993 >>11508944 This is fucking with my mind. Tilting an infinite ruler like this, the laws of perspecive means that you can see the entire ruler. I can see intinity? Whoa, dude.

Anonymous Sat Mar 28 10:05:36 2020 No.11508995

>>11508933
construct two sets:
A: the set of all integers
B: the set containing the result of [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math]
>[math]A: [ \underbrace{0 , 1 , 2 , 3 , 4 , \dots}_{size = \infty} ] [/math]
>[math]B: [ \underbrace{0 . 9 , 9 , 9 , 9 , \dots}_{size = \infty} ] [/math]
let n'th element in A have a directly comparable element in B such that [math]sum_{n=1}^{\infty} \frac{9}{10^n}[/math] maps to [math]n[/math] in A and B.
let [math]n[/math] be any number
https://www.wolframalpha.com/input/?i=is+infinity+a+number%3F

Now that this is laid out, what information can be gleamed from this?
the most of which has occurred is two arbitrarily undefined evergrowing sets of numbers have been created and some kind of cheat was used to "definitely" contain them between and opening and closing bracket, defying the definition of infinity being "unbounded".
the useful bits however, are
> "n is any number"
> "[math]\infty[/math] is not a number"
which predicates that any usage of our sets to retrieve a calculable value from B must be an n'th equivalent term of the n'th element from A.
and since n = a number
and infinity = not a number
the usage strictly applies finitely.
for any n, in A or B applying to [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math], there is a non-zero smallest part [math]\frac{1}{10^n}[/math] which exists.

Anonymous Sat Mar 28 10:06:12 2020 No.11508997

>>11508969
reasonably, it's a dumb ass way of writing a meaningless digit
anything after the "...", aka ellipsis indicates the previous digit repeats forever
so if you have to tack something on the right side of ..., it's either meaningless or literally infinitely small - the value of n in that position is n*10^-inf=0

>>	Anonymous Sat Mar 28 10:06:19 2020 No.11508999 >>11508989 I think the intepretation of finitely many digits is much more reasonable.

>>	Anonymous Sat Mar 28 10:07:15 2020 No.11509000 >>11508999 >>11508949

>>	Anonymous Sat Mar 28 10:09:31 2020 No.11509005 >>11508997 >>11508949 >>11509000 >t. second year math major

Anonymous Sat Mar 28 10:11:04 2020 No.11509008
File: 38 KB, 553x241, xHbYo[1].png [View same] [iqdb] [saucenao] [google]

>>11508993
parabola is an ellipse with one focal point being an ideal point. why? if you draw a parabola on an infinite canvas and tilt it, you'll see an ellipse. how cool is that?

Anonymous Sat Mar 28 10:13:23 2020 No.11509012

>>11508995
>defying the definition of infinity being "unbounded".
Only if you don't know what unbounded means.

> "n is any number"
> "∞ is not a number"
>which predicates that any usage of our sets to retrieve a calculable value from B must be an n'th equivalent term of the n'th element from A.
Doesn't follow.

>for any n, in A or B applying to ∑∞n=1910n, there is a non-zero smallest part 110n which exists.
Mmhmm but we are not interested in some n but the entire sum.

>>	Anonymous Sat Mar 28 10:14:32 2020 No.11509014 >>11509008 Tha is cool

>>	Anonymous Sat Mar 28 10:16:26 2020 No.11509018 >>11508995 You could have just said "any partial sum is not 1" instead of wasting all that time writing out an irrelevancy. Brainlet.

>>	Anonymous Sat Mar 28 10:18:34 2020 No.11509019 File: 418 KB, 479x720, tips fedora.png [View same] [iqdb] [saucenao] [google] >>11509012 apparently you don't know what boundaries are.

>>	Anonymous Sat Mar 28 10:18:47 2020 No.11509020 >>11509005 it's comfy here https://www.wolframalpha.com/input/?i=%289.9...7%29-10

>>	Anonymous Sat Mar 28 10:21:58 2020 No.11509031 >>11509019 What is the largest natural number?

>>	Anonymous Sat Mar 28 10:22:12 2020 No.11509032 >>11509020 truly topthink of the toppest thinkers. https://www.wolframalpha.com/input/?i=sum%5B9%2F10%5En%2C+%7Bn%2C1%2C10%5E140%7D%5D+-+1

>>	Anonymous Sat Mar 28 10:23:36 2020 No.11509035 >>11509031 Didn't know we were playing Jeopardy but yes, that's 200 points for "retarded questions"

>>	Anonymous Sat Mar 28 10:24:41 2020 No.11509037 >>11509031 (undefined)

>>	Anonymous Sat Mar 28 10:25:05 2020 No.11509038 >>11509032 >syntax error kek, am I supposed to applaud?

>>	Anonymous Sat Mar 28 10:26:51 2020 No.11509041 >>11509037 So how you can we talk about the natural numbers as a thing? It's boundless, so we can't talk about them. How many real numbers are there between 0 and 1?

>>	Anonymous Sat Mar 28 10:27:52 2020 No.11509045 >>11509041 >How many real numbers are there between 0 and 1? aleph-1

>>	Anonymous Sat Mar 28 10:30:07 2020 No.11509049 >>11509020 It's allright. Next year you'll begin developing a deeper understanding of concept, so you won't have to get so hung up on notation.

>>	Anonymous Sat Mar 28 10:31:12 2020 No.11509053 >>11509041 >It's boundless, so we can't talk about them. I don't see how that follows.

Anonymous Sat Mar 28 10:34:50 2020 No.11509064

>>11509041
as many as you're willing to calculate.
sky's the limit.
you can come up with unlimited possibilities between 0.5 and 1.0 just using [math]lim_{k \rightarrow \infty} \sum_{n=1}^{\infty} \frac{k}{(k+1)^n}[/math], and yet it wouldn't even be all the possibilities between 0.5-1.0

think about that.
there are more real numbers between 0.5->1.0 than the already infinite possibilities between 0.5 -> 1.0 which [math]lim_{k \rightarrow \infty} \sum_{n=1}^{\infty} \frac{k}{(k+1)^n}[/math] has the capacity to account for.

infinity > infinity.

>>	Anonymous Sat Mar 28 10:36:59 2020 No.11509067 >>11509045 Impossible, it has to be finite since they ate bounded by 0 and 1. Apparently you don't know what boundaries are.

>>	Anonymous Sat Mar 28 10:37:03 2020 No.11509068 File: 660 KB, 1432x4127, math.jpg [View same] [iqdb] [saucenao] [google] >>11508414 yes

Anonymous Sat Mar 28 10:37:35 2020 No.11509069
File: 155 KB, 1300x957, external-content.duckduckgo-7.jpg [View same] [iqdb] [saucenao] [google]

>>11508944
>we can see that the points Z and W actually coincide, BZ and BW coincide, and therefore slope of BZ is 0. which proves 0.999... = 1.

You just assumed that 1=0 in order to get the conclusion you wanted! You know that railroad tracks don't ACTUALLY converge in the distance, right?

>>	Anonymous Sat Mar 28 10:38:01 2020 No.11509070 >>11509053 Then why are you saying it?

>>	Anonymous Sat Mar 28 10:39:11 2020 No.11509074 >>11509064 No that must be wrong, since they are bounded by 0 and 1 and as you said this violates the definition of unbounded.

>>	Anonymous Sat Mar 28 10:40:39 2020 No.11509077 >>11509074 "as many as you're willing to calculate" is implicitly a finite amount. just wordplay.

>>	Anonymous Sat Mar 28 10:40:57 2020 No.11509079 >>11509070 I'm... not?

>>	Anonymous Sat Mar 28 10:43:21 2020 No.11509084 >>11509031 My ass

>>	Anonymous Sat Mar 28 10:47:33 2020 No.11509094 I wonder if OP ever understood the proofs in this thread.

>>	Anonymous Sat Mar 28 10:59:43 2020 No.11509119 >>11509020 >>11509032 https://www.wolframalpha.com/input/?i=penis+on+an+English+keyboard wolfram is truly a bountiful wealth of knowledge

>>	Anonymous Sat Mar 28 11:10:32 2020 No.11509138 >>11509077 Finite, but unbounded. Thanks for proving my point.

>>	Anonymous Sat Mar 28 11:11:10 2020 No.11509140 >>11509067 kek, oh anon https://youtu.be/i7c2qz7sO0I?t=4m20s

>>	Anonymous Sat Mar 28 11:16:46 2020 No.11509151 >>11509049 a mathematician not strict on notation is not a mathematician

>>	Anonymous Sat Mar 28 11:18:17 2020 No.11509157 >>11509151 Spoken like a true second year math major.

>>	Anonymous Sat Mar 28 11:19:58 2020 No.11509163 >>11509068 >confusing x and f(x) yet again, not surprised

>>	Anonymous Sat Mar 28 11:21:07 2020 No.11509168 >>11509069 >You know that railroad tracks don't ACTUALLY converge in the distance, right? how is that relevant ? who said anything about convergence ?

>>	Anonymous Sat Mar 28 11:21:54 2020 No.11509171 >>11509157 >graduating is an alien concept to you have a great life anon

>>	Anonymous Sat Mar 28 11:23:00 2020 No.11509175 >>11508057 Checks out.

>>	Anonymous Sat Mar 28 11:31:10 2020 No.11509196 >>11507816 error in rounding... 1/3=0.333333333333 2/3=0.666666666667 ------------------------------- 3/3=1 To be clear. "..." is not real 1/3 is not a rational real number /sci/ is gay

>>	Anonymous Sat Mar 28 11:43:46 2020 No.11509234 >>11509196 retard

>>	Anonymous Sat Mar 28 11:50:25 2020 No.11509251 >>11509234 What I mean is: three dots in a row are abstract, whereas real numbers are real, and 1/3 is neither.

Anonymous Sat Mar 28 11:50:47 2020 No.11509252

>>11509196
Thats the deal though. Lots of rounding occurs in computable math. There is some "soft" idea that after x amount decimal digits, it's okay to just cut it at x+1 and use the x+1'th digit to potentially round the x'th.
it can solve some logical errors, such as
>1 ÷ 3 = "0.3333333" (Answer)
>(Answer) × 3 = "1.0"
because it will round the last digit,
but at the same time it creates logical problems elsewhere where rounding isn't what's desired.

What is the mathematical law or rule that you're supposed to ignore digits longer than 10 decimals while using the 11th digit to round and carry to the 10th?

>>	Anonymous Sat Mar 28 11:52:48 2020 No.11509254 >>11509252 But, but, TI80 is my friend.

>>	Anonymous Sat Mar 28 11:58:19 2020 No.11509265 File: 29 KB, 398x369, ANUDDA SHOAH.png [View same] [iqdb] [saucenao] [google] >>11509252

Anonymous Sat Mar 28 12:00:29 2020 No.11509269

>>11509251
This still doesn't make sense.
Real numbers are real numbers.
1/3 is a real number. The symbol "1/3" is a representation of that number in a fractional form. The symbol "0.333..." is another representation of the same number, in an infinite decimal expansion form.

Anonymous Sat Mar 28 12:10:20 2020 No.11509293

>>11509269
1/3 is a real number but the infinite decimal expansion isn't actually equal to it. just "close enough" depending on how you look at it. more literally, 1/3 is greater than the decimal expansion.

and depending on how you look at that inequality, 1/3 and "0.3333..." are actually different numbers.

>>	Anonymous Sat Mar 28 12:13:49 2020 No.11509299 >>11509293 infinite decimal expansion is actually equal to it. finite decimal expansion isn't actually equal to it.

>>	Anonymous Sat Mar 28 12:15:46 2020 No.11509305 >>11509265 fuck off back to >>>/pol/

Anonymous Sat Mar 28 12:16:59 2020 No.11509310

>>11509299
infinite is finite.

another way of looking at it is >>11508995 which shows infinite is just a direction of continued finite effort.

there is no direct equality without an end to the decimal expansion, and infinite decimals doesn't produce an end, so it doesn't produce direct equality.

>>	Anonymous Sat Mar 28 12:17:43 2020 No.11509314 >>11509293 You need to be 18 to browse this website

>>	Anonymous Sat Mar 28 12:18:08 2020 No.11509315 >>11509310 lol wat

>>	Anonymous Sat Mar 28 12:19:16 2020 No.11509319 >>11509293 What you're saying is only true for finite decimal expansions of arbitrary lengths. The whole point about the infinite decimal expansion is that it coincides with the limit of the finite decimal expansions.

>>	Anonymous Sat Mar 28 12:20:28 2020 No.11509321 >>11509319 okay bigdick, what's the limit of the finite decimal expansions? the biggest real number? whats the biggest real number? oh right, there isn't one. get fucked.

>>	Anonymous Sat Mar 28 12:21:25 2020 No.11509324 >>11509321 >okay bigdick, what's the limit of the finite decimal expansions? It's the least real number that is not smaller than any of the finite decimal expansions.

>>	Anonymous Sat Mar 28 12:23:41 2020 No.11509330 >>11509319 >>11509321 >>11509324 lmao u guys

>>	Anonymous Sat Mar 28 12:24:12 2020 No.11509332 0.999... = 1 but ONLY if you round on the last digit of 0.999...

>>	Anonymous Sat Mar 28 12:29:36 2020 No.11509349 >>11509321 The limit of the finite decimal expansions in question: 0.3 0.33 0.333 0.3333 0.33333 0.333333 and so on... is 1/3.

>>	Anonymous Sat Mar 28 12:31:43 2020 No.11509359 >>11509310 >infinite is finite wew lad

Anonymous Sat Mar 28 12:35:01 2020 No.11509369

For anyone who claims 0.999...=/=1
Define FORMALLY what you mean by:
- 0.999...
- 1
The mathematicians here who claim 0.999...=1 use the standard implicit definition
- 0.999... is the real number represented by the Cauchy sequence (0, 0.9, 0.99, 0.999, ...)
- 0.9999... = 1 asserts that the Cauchy sequences for 1, namely (1,1,1,...) is equivalent to the Cauchy sequence of (0.9, 0.99, 0.999, ..)

>>	Anonymous Sat Mar 28 12:35:30 2020 No.11509370 >>11509310 >there is no direct equality without an end to the decimal expansion This is simply not true.

Anonymous Sat Mar 28 12:41:26 2020 No.11509385

>>11509349
[math]\sum_{n=1}^{k} \frac{3}{10^n}[/math]

k = the limit.

limit is a qualia of the direction component within the equation, not within the result.

but if you want to say 1/3 is the limit of the decimal expansion "0.3333...", then... well, that doesn't really mean much other than what you're saying. Doesn't mean they're equal. it's sure enough to say that "0.333..." is trying it's darndest to reach it's limit of 1/3, but the fact of the matter is it never will, because that's what infinity evokes. never-ending.

>>	Anonymous Sat Mar 28 12:42:28 2020 No.11509389 >>11509370 prove it

>>	Anonymous Sat Mar 28 12:44:36 2020 No.11509402 >>11509389 >>11508140

>>	Anonymous Sat Mar 28 12:46:25 2020 No.11509408 >>11508389 substraction, faggot

>>	Anonymous Sat Mar 28 12:48:07 2020 No.11509412 >>11507816 it's not 0.999 is 0.999 and 1 is 1 you damn cunt

Anonymous Sat Mar 28 12:54:46 2020 No.11509437

>>11508833
>what you're saying is not a reasonable math function without first addressing how you're creating your 0.999.... reference.
>what the fuck infinity means and what the fuck "..." dot repetition means, of which neither are explained well or used correctly.
Decimal expansion tells you where you find a number on the number line if you keep dividing line segments into smaller and smaller parts. Nothing else. So denote [math]x = 0.999.\dots[/math] and let's get into it.

The number before the decimal point being zero literally means that [math]x \in [0,1][/math].
The first digit being 9 literally means that if you divide [math][0,1][/math] into ten equal parts, then [math]x[/math] is somewhere in the tenth part. In other words [math]x \in [\tfrac{9}{10},\tfrac{10}{10}][/math]
The second digit being 9 literally means that if you divide the smaller segment [math][\tfrac{9}{10},\tfrac{10}{10}][/math] into ten equal parts, then [math]x[/math] is somewhere in the tenth part. In other words [math]x \in[\tfrac{99}{100},\tfrac{100}{100}][/math]
The third digit being 9 literally means that if you divide the smaller segment [math][\tfrac{99}{100},\tfrac{100}{100}][/math] into ten equal parts, then [math]x[/math] is somewhere in the tenth part. In other words [math]x \in[\tfrac{999}{1000},\tfrac{1000}{1000}][/math]
The fourth digit being 9 literally means that if you divide the smaller segment [math][\tfrac{999}{1000},\tfrac{1000}{1000}][/math] into ten equal parts, then [math]x[/math] is somewhere in the tenth part. In other words [math]x \in[\tfrac{9999}{10000},\tfrac{10000}{10000}][/math]
...
The n-th digit being 9 literally means that if you divide the smaller segment [math][ \sum_{k=1}^{n-1} \tfrac{9}{10^k},1 ][/math] into ten equal parts, then [math]x[/math] is somewhere in the tenth part. In other words [math]x \in [ \sum_{k=1}^{n} \tfrac{9}{10^{k}},1 ] [/math]
...

>>	Anonymous Sat Mar 28 12:55:17 2020 No.11509439 >>11509408 By your logic 10x=10000 -x=1 9x=999 x=111

Anonymous Sat Mar 28 12:56:34 2020 No.11509445

>>11508833
>>11509437
>what you're saying is not a reasonable math function without first addressing how you're creating your 0.999.... reference.
>what the fuck infinity means and what the fuck "..." dot repetition means, of which neither are explained well or used correctly.
The dots in [math]x = 0.999\dots[/math] are not "hiding anything." All they're saying is that the n-th digit of this decimal expansion is 9.

Obviously we will never find [math]x[/math] if we attempt to actually follow these instructions, because there is no last step. We will always end up only with a very small interval which contains [math]x[/math]. There will always be one more step to perform.

HOWEVER. That doesn't mean we can't find [math]x[/math] by other means. [math]x[/math] is simply a point on the number line which satisfies [math]x \in [ \sum_{k=1}^{n} \tfrac{9}{10^{k}},1 ] [/math] for all [math]n \in \mathbb{N}[/math]. That is:
[eqn]\sum_{k=1}^{n} \tfrac{9}{10^{k}} \leq x \leq 1 \quad \text{for all }n \in \mathbb{N}[/eqn]
All we need are these two facts:
Firstly, there exists AT LEAST one number with this property and that's [math]1[/math].
Secondly, there cannot be two distinct numbers with this property.

These two together give [math]x=1[/math].

[math]0.999\dots[/math] was just a very stupid and very inefficient set of instructions on how to find one on the number line.

Anonymous Sat Mar 28 12:57:45 2020 No.11509452

>>11509385
>k = the limit.
wat? You're not making sense.

>if you want to say 1/3 is the limit of the decimal expansion "0.3333..."
That strictly speaking not what I'm saying.
What i'm saying is 0.333... is the limit of (0.3, 0.33, 0.333, ...). I'm also saying 1/3 is the limit of the same sequence (0.3, 0.33, 0.333, ...).

>the matter is it never will, because that's what infinity evokes. never-ending.
The never-ending thing about the infinite decimal expansion is the number of decimals, not the amount of time it would take to write out all the decimals one after the other.
The infinite decimal expansion is not a process. It is a symbolic representation of a real number.

>>	Anonymous Sat Mar 28 12:58:30 2020 No.11509455 >>11508411 >you think infinitellty small numbers exist. They dont by your logic, an infinite amount of dots wouldnt form a line

>>	Anonymous Sat Mar 28 13:00:54 2020 No.11509462 >>11509437 ooooooohhh shitlatexman is back what happened, did they kick you out of the psychic ward to use it for corona-patients?

>>	Anonymous Sat Mar 28 13:01:49 2020 No.11509465 >>11509452 you're just making shit up and its easy to see.

>>	Anonymous Sat Mar 28 13:05:12 2020 No.11509478 Thats why you use base 6, the base where the least % of all single digit divisions are repeating decimals

Anonymous Sat Mar 28 13:10:52 2020 No.11509501

>>11509465
I'm trying to discuss the concept of infinite decimal expansion and symbolic number representation, without obfuscating the matter with formalism. Other anons are more suited to and have already shown the formal explanations. I'm more interested in the ideas behind the formalism.

>>	Anonymous Sat Mar 28 13:14:12 2020 No.11509509 >>11508503 >I can just keep adding stuff on the smaller side of a "greater than" symbol and the symbol will stay true 2 > 1 2 > 1.5 2 > 2 woooooooooow, mathfags btfo

>>	Anonymous Sat Mar 28 13:17:55 2020 No.11509523 >>11509455 Please explain your thinking here. I don't follow.

>>	Anonymous Sat Mar 28 13:20:30 2020 No.11509534 File: 9 KB, 250x153, Population_of_Armenia_since_1949.svg.png [View same] [iqdb] [saucenao] [google] >>11509265 >population growth rates are constant >population growth rates are unaffected by genocide I guess the Armenian genocide is fake too.

Anonymous Sat Mar 28 13:25:36 2020 No.11509554

>>11509501
never-ending means the same thing regardless if time is a factor or not. the decimal "0.333..." is never-ending.

Relative to trying to translate 1/3 to decimal via division, the never-ending nature is an emergent property of being unable to settle on a final digit (which is otherwise present in decimal forms of fractions that do evenly divide, such as 1/2, 1/4, 1/5, 1/8, 1/10, etc)
Relative to [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math], the never-ending nature is an emergent property of using "[math]\infty[/math]" as an element of the function towards solving the equation.
In the Sum, we get the answer we are telling it to give us cleanly, and we expect it to never-end because that's a supplied element from the get-go. so [math]\sum_{n=1}^{\infty} \frac{3}{10^n} = 0.333\dots [/math], and this is also the same exact number retrieved from attempting to translate 1/3 into decimal.

[math]\frac{1}{3} > (\sum_{n=1}^{\infty} \frac{3}{10^n} = 0.333\dots )[/math]

>>	Anonymous Sat Mar 28 13:30:59 2020 No.11509582 >>11509554 imagine losing in math to a 8-year-old

Anonymous Sat Mar 28 13:48:35 2020 No.11509649

>>11509452
Infinity is not a number though. It isn't used to describe a "set-in-stone" amount the same way you'd say there are 10 apples, 7,000,000,000 people, or 365 days in a year.
10; 7,000,000,000; 365; these are all numbers used to describe amounts.
Infinity isn't a number though, so it can't be used the same way.
Infinity isn't "set-in-stone" like 10 is.
10 apples, 10 people, 10 days; regardless of what is being counted, if there are 10 countable elements, then you'll have 10, distinct from 9 or 11.

refer to >>11508995 where the size of the set A is noted. Infinite size here is not some extension of the numberline, but rather it encompasses the numberline. "1", "2", or "10" are all elements within infinity, and not merely in the sense that "1, 2, and 10 are all elements of 13" as if they're implicitly being added together. The never ending possibilities of increasingly large integers greater than 0 are what define infinity.
To say "0.999..." has "infinity 9's" is to say it simultaneously has all consecutive finite counted elements listed within the "infinite" set. But given there is no indication of how all these elements are being simultaneously invoked, be they adding/multiplying/factorializing/etc, (aka 1+2+3+... / 1×2×3×... / etc), then theres no honest sensible approach, and given trying to define "all" elements of something that never-ends, it's even less intelligible. "All" elements of a set with 10 elements is 10. "All" elements of a set with unlimited elements is... not a knowable number.

>>	Anonymous Sat Mar 28 13:51:17 2020 No.11509657 >>11509534 the armenian genocide happened in WW1. your graph starts after WW2.

Anonymous Sat Mar 28 13:52:54 2020 No.11509663

>>11509554
There is nothing in what you said that implies your conclusion that
[math]
\frac{1}{3} > \sum_{n=1}^{\inf}\frac{3}{10^n}
[/math]
which is false.

Also fun fact: Did you know that the infinite decimal exansion 0.000... is equal to to finite decimal expansion 0.0 which is equal to the integral form 0?

>>	Anonymous Sat Mar 28 13:52:56 2020 No.11509664 >>11509582 you must be 18+ to post here.

Anonymous Sat Mar 28 13:58:46 2020 No.11509683

>>11509663
Repeating decimal 0's are an emergent property of final solution.
1/2 = 0.50000000...
1/4 = 0.25000000...
1/8 = 0.12500000...
1/10 = 0.1000000...
Repeating decimal zero's are defacto a sign of final equality because the steps of long division to reach that point technically end.
1/8 = 0.125 is the technical final step, and anything further is just solving [math]0-0 = 0 -0 = 0 -0 ...[/math] pointlessly.

>>	Anonymous Sat Mar 28 13:58:57 2020 No.11509685 >>11509649 >Infinity is not a number though. I never said it was. >"All" elements of a set with unlimited elements is... not a knowable number. I never said anything like this either. But that does not mean we can't refer all elements in a set.

>>	Anonymous Sat Mar 28 14:01:17 2020 No.11509693 >>11509663 1/3 > 0.3; true 1/3 > 0.33; true 1/3 > 0.333; true if this continues, it will always remain the same true case. ... 1/3 > 0.333...; true

>>	Anonymous Sat Mar 28 14:07:21 2020 No.11509708 >>11509693 Wrong, review the order limit theorem. You can only conclude that 1/3 >= 0.33333....

Anonymous Sat Mar 28 14:07:51 2020 No.11509709

>>11509693
>if this continues, it will always remain the same true case.
this is simply not true. it's a common beginner mistake, that doesn't make it acceptable.
[math]a_n < K[/math] for all [math]n[/math] only implies [math]\lim_{n\to\infty}a_n \leq K[/math]
[math]x < K[/math] for all [math]x \in A[/math] only implies [math]\sup A \leq K[/math]

>>	Anonymous Sat Mar 28 14:08:38 2020 No.11509710 >>11509693 >>11509509

Anonymous Sat Mar 28 14:08:38 2020 No.11509711

>>11509683
>steps of long division to reach that point technically end
No they don't. They technichally do not end. It is precisely because they technically do not end that I'm able to continue adding zeroes at the end. There simply come a point where it's convenient to stop, because continuing repeating self similar steps just doesn't yield any additional information.

But this whole talk about step of an algorithm is a red herring, because as I said earlier, a decimal expansion (finite or infinite) is not a process. It is a symbol that refers to a real number.

>>	Anonymous Sat Mar 28 14:08:50 2020 No.11509712 >>11509657 Way to miss the point. The graph must be fake since population growth rates are constant, right?

>>	Anonymous Sat Mar 28 14:11:44 2020 No.11509727 >>11509693 >if this continues, it will always remain the same true case. Not true. Only true for finite decimal expansion 0.3, 0.33, 0.333 etc. Like I'm sure I said in an earlier post. I don't think you understand how limits work.

Anonymous Sat Mar 28 14:13:04 2020 No.11509733

>>11509685
>I never said it was
>>11509452
>>The never-ending thing about the infinite decimal expansion is the [math]\text{number of decimals}[/math]
>>The infinite decimal expansion... is a symbolic [math]\text{representation of a real number}[/math].
>i never said it was
sounded to me like you were using infinity as a number.

>>	Anonymous Sat Mar 28 14:17:50 2020 No.11509744 >>11509664 classic projection

Anonymous Sat Mar 28 14:21:16 2020 No.11509753

>>11509727
0.3 has how many 3's?
0.33 has how many 3's?
0.333 has how many 3's?
loose answer: a finite amount.

0.333... has how many 3's?
>infinity is not a number
loose answer: an arbitrary finite amount.

I don't think you understand what infinity means. It's analogous with continuous; never-ending.

If you had infinite time to increment from 0 by +1 every second, which case is true?
>a: after an infinite amount of time has passed, you'll have counted through all the integers
Or
>b: you will count finite numbers forever and never stop

Anonymous Sat Mar 28 14:23:25 2020 No.11509756

>>11509733
Ok, fine. I did use the word 'number' in reference to an infinite sequence. Would you have felt more comfortable if I had said
"cardinality of the set of decimal places"?

The point i was trying to make is that anon apparently thinks about infinity as steps of an algorithm that takes time to carry out and must be carried out sequentially.

>>	Anonymous Sat Mar 28 14:25:10 2020 No.11509764 >>11507839 presupposes 0.999...*10=9.999... to begin with

>>	Anonymous Sat Mar 28 14:26:11 2020 No.11509768 >>11509756 everything is carried out sequentially. merely existing to have this retarded argument required a sequence of events. the real question is at which point you're going to figure it out.

Anonymous Sat Mar 28 14:26:43 2020 No.11509771

>>11509753
>an arbitrary finite amount
Wrong again. Arbitrarily large finite =/= infinite. Finite induction does not prove the infinite case.
As an example, you can prove inductively that an arbitrary finite intersection of open sets remains open, but it's easy to construct an infinite intersection that isn't open

Anonymous Sat Mar 28 14:35:09 2020 No.11509790

>>11509753
Again, the infinite decimal expansion is not a process that must be carried out.

In the same sense that the infinite set of natural numbers is not a timed process that must be carried out.
I can refer to, and think about, the entire infinite set in a finite constant amount of time without having to process each individual element sequentially.

Similarly a sequence does not need to 'arrive' at a limit by way of processing each element successively in order for us to know that the limit exists and what it is.

Anonymous Sat Mar 28 14:36:50 2020 No.11509797
File: 83 KB, 384x313, eQ20E.jpg [View same] [iqdb] [saucenao] [google]

>>11509771
Arbitrarily finite is the measure that can be applied to infinite. It's not that they're not the same and yet permiss the same function. Its that arbitrary finite is the ruler and infinite is the stick. Arbitrary finite is what you can measure and infinite is the thinf you're measuring.
They're not the same cause they're not the same function.

refer back to
>>b: you will count finite numbers forever and never stop
if during this process, someone else asked you what number you were on, you would tell them what number you're on and it would be an arbitrary finite number.
To take a measurement is essential to solving something.
If instead you didn't say which number you were on cause you're intent on "reaching infinity", then whatever value's you're enumerating through will never be useful for anything and your non-response is no better or worse than shrugging or replying with "???".

>how many 3's do we need to calculate on 0.333...?
>"???"
>aight thanks bud

>>	Anonymous Sat Mar 28 14:37:37 2020 No.11509800 >>11509764 True. It is a reasonable supposition though.

>>	Anonymous Sat Mar 28 14:37:59 2020 No.11509801 >>11509797 >They're not the same cause they're not the same function. >function you keep using this word and I don't think you know what it means

>>	Anonymous Sat Mar 28 14:38:42 2020 No.11509803 >>11509768 >everything is carried out sequentially Not in mathematics.

>>	Anonymous Sat Mar 28 14:41:00 2020 No.11509810 File: 267 KB, 534x588, 1551554622542.png [View same] [iqdb] [saucenao] [google] >>11509790 >>11509771 >>11509801 >>11509803 >mouthbreathers

Anonymous Sat Mar 28 14:41:23 2020 No.11509811

>>11507933
>>11507960
There world is constrained by a base_n number system, in which case 1/3 always is represented by some irrational repeating number.
>>11508411
>you know that 1/3=0.333...
is equivalent to
>you know that 1=0.999...
Also, pathetic need of the additional assumption that I wouldn't catch this language.
>>11509800
It isn't reasonable to use that supposition in a proof of the same thing. It's circular reasoning to presuppose 0.999...=1, in order to then prove that 0.999...=1

Anonymous Sat Mar 28 14:43:46 2020 No.11509818

>>11509797
You don't measure the infinite with the arbitrary. Instead, you use the arbitrary to show that the infinite can't be measured, and hence show that the infinite must be treated distinctly from the finite. To "measure" or reason about the infinite, you have to use analysis to build a toolkit from the ground up, instead of relying on the tools of the finite that no longer logically apply.

Anonymous Sat Mar 28 14:47:44 2020 No.11509827

>>11509771
0.333... has how many 3's?
>infinity is not a number
what is your answer?
you disagree that it isn't an arbitrary finite amount, but at the same time "infinite" is not a number, and is therefore not applicable to being a number amount. You also disagree the decimal expansion "0.333..." must continue or expand from something. So how do you answer?
0.333... has how many 3's?

Anonymous Sat Mar 28 14:51:34 2020 No.11509833

>>11509827
Your question does not have a defined answer, since the naturals and reals only consist of finite elements. If you'd permit the use of the extended reals, I could give you an answer, but it cannot be a natural or real number, which is what you're looking for.

>>	Anonymous Sat Mar 28 14:52:54 2020 No.11509836 >>11509833 >>11509818 Or another logically consistent answer could be, "the set of threes has the same cardinality as the naturals."

Anonymous Sat Mar 28 14:55:30 2020 No.11509847

>>11509827
your dogma is that "infinity is not a number" and that a question starting with "how many ..." must have a number for an answer. if you insist on this, then your question doesn't have an answer. it's like pointing to a chair and asking "what animal is this?"

Anonymous Sat Mar 28 15:01:27 2020 No.11509861

>>11509833
I think i understand your logic.
Consider inter-mantissa.
>[math] 0.0 < 0.1 < 0.\bar{1} < 0.2 < 0.\bar{2} < 0.3 < 0.\bar{3} < 0.4 < 0.\bar{4} < 0.5 < 0.\bar{5} < 0.6 < 0.\bar{6} < 0.7 < 0.\bar{7} < 0.8 < 0.\bar{8} < 0.9 < 1.0[/math]
you would have that a value [math]\frac{1}{3}[/math] cleanly and decisively equals [math]0.\bar{3}[/math] much the same way that [math]\frac{1}{2} = 0.5[/math]. Put another way, as 0.5 has arbitrary 0's after it denoting full equality and final solution, you would have [math]0.\bar{3}[/math] also be seen in a similar manner. That after this "symbol 3" value, there also exists some imaginary metric of arbitrary 0's denoting final solution and full equality to [math]\frac{1}{3}[/math].

I'm like 90% sure this is what you're trying to convey.

>>	Anonymous Sat Mar 28 15:11:05 2020 No.11509884 >>11509861 The metric I'm using is "a=b iff abs(a-b) < r for all real r>0"

Anonymous Sat Mar 28 15:12:47 2020 No.11509887

>>11509811
>It isn't reasonable to use that supposition in a proof of the same thing. It's circular reasoning to presuppose 0.999...=1, in order to then prove that 0.999...=1
You're right in that the supposition 10*0.999... = 9.99... needs to be proven formally or the rest doesn't count as a proof.
But the first time I encountered this 'proof' I arrived at the above supposition based on my knowledge about how multiplication with decimal numbers worked that had been taught, and some reasonable assumptions about how that might extend to multiplication by 10 with infinite decimals.
I did not need to presopose 0.999...=1 to arrive at the conclusion that 10*0.999... = 9.99...
Instead, based on my guess that 10*0.999... = 9.99... I arrived at the conclusion that 0.999...=1, wich blew my mind at the time. It might be thought of as a sort of "high level" proof that takes for granted som seemingly obvious assumptions, but hinges on those assumptions in fact being correct. You know, like most of education and knowledge. Or if not a proof then a strong indicator.

But yeah, the most stringent proof of 10*0.999... = 9.99... that I know is the proof by limits, which is essentially the same as proving 0.999...=1 directly.

>>	Anonymous Sat Mar 28 15:13:42 2020 No.11509888 >>11509811 In base 3, 1/3 = 0.1

Anonymous Sat Mar 28 15:32:06 2020 No.11509924

>>11509847
I would consider it more like taking a photo. If i said "hey, turn around and take a photo!" And you immediately turned around and took a photo (for the sake of convenience, its a polaroid and prints instantly), will you actually know what's going to show up on the photo before you see the photo? You were facing the opposite direction the moment before the photo was taken, so you had no idea what was going on behind you. What things were moving, where things were moving towards, it's literally quite a mystery to you until the photo prints and shows you a vertical slice of what was occurring. But once you have your photo, your snapshot, your measure of a moment, you can definitely tell what things were moving and where they were moving towards when comparing the photo to things as they unfold.

What i'm saying is, a photo is a finite measurable freeze-frame of the expansion of time since before last thursday. Much the same as 1/3 = ??? becomes 1/3 = 0.333... once you make the measurement.

If you solve it via long division (0.333...) well those repeating 3's tend toward a finite end because you'll either get bored of writing 3's or decide a certain amount of decimal digits is enough.
If you solve it via magical numbers ([math]0.\bar{3}[/math]) gets rendered instantly (like [math]\frac{1}{2} = 0.5[/math] is instant), but now you have to explain where magical numbers come from and why they need to exist.

Anonymous Sat Mar 28 15:33:14 2020 No.11509927 [DELETED]

>>11509924
>cont.
I'll have you know that these inter-mantissa magical numbers, provided the accomodation in >>11509861 where
>after this "symbol n" value, there also exists some imaginary metric of arbitrary 0's denoting final solution and full equality inherently implies a couple things, such as there is an end to the 3's (they're not "infinite") so 0's can come after, and if 0's come after, would require [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math] produce those 0's at [math]n=\infty[/math] for [math] \frac{3}{10^{\infty}} = 0[/math] which requires infinity be a sequentially reachable number incrementing from a real number, which means it's also a finite end to the numbers, and then suddenly literally everything you believe in is so fucking mind-fuckingly retarded that it required this entire thread to explain to you why what you vehemently defend as true is instead actually just fucking fanfiction.

Anonymous Sat Mar 28 15:36:32 2020 No.11509930

I'll have you know that these inter-mantissa magical numbers, provided the accomodation in >>11509861 where
>after this "symbol n" value, there also exists some imaginary metric of arbitrary 0's denoting final solution and full equality
inherently implies a couple things, such as there is an end to the 3's (they're not "infinite") so 0's can come after, and if 0's come after, would require [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math] produce those 0's at [math]n=\infty[/math] for [math] \frac{3}{10^{\infty}} = 0[/math] which requires infinity be a sequentially reachable number incrementing from a real number, which means it's also a finite end to the numbers, and then suddenly literally everything you believe in is so fucking mind-fuckingly retarded that it required this entire thread to explain to you why what you vehemently defend as true is instead fucking fanfiction.

Anonymous Sat Mar 28 15:48:07 2020 No.11509957

>>11509924
>If you solve it via long division (0.333...)
But you can never do that. Solving it via long division you will never arrive att 0.333... because that would require infinite positive-time steps, i.e. infinite time. What you can do is realise that you're repeating self-similar steps, so you can conlude what the limit number looks like. You can therefore shortcircuit the process and arrive at an infinite decimal number expansion in a finite time. And that's where the magic number comes from.

>>	Anonymous Sat Mar 28 15:53:23 2020 No.11509972 >>11509957 >lets pretend infinite is finite

>>	Anonymous Sat Mar 28 15:57:14 2020 No.11509979 >>11509827 >0.333... has how many 3's? aleph-0

>>	Anonymous Sat Mar 28 16:02:32 2020 No.11509998 >>11509972 How do you even have problem with this? If you keep recursively performing self similiar steps that result in a three, you know you're not suddenly going to get a four at some decimal place.

Anonymous Sat Mar 28 16:12:54 2020 No.11510020

>>11509452
>>the matter is it never will, because that's what infinity evokes. never-ending.
>The never-ending thing about the infinite decimal expansion is the number of decimals, not the amount of time it would take to write out all the decimals one after the other.

i think there was a momentary split of coherence here. You seemed to think "never" was a function of time, but it's just as easily conveyed via a single-notion comparison of "is" or "is not"
if "1 is never 2", it means the same as
"1 is not 2"

so if "0.333..." is 'trying it's darndest to reach 1/3', the emergent property of there being unending 3's means it never actually reaches 1/3.
>0.333... is never 1/3
>0.333... is not 1/3

>>	Anonymous Sat Mar 28 16:18:31 2020 No.11510036 >>11508259 9.99999... = 10 99.9999... = 100 and so on

Anonymous Sat Mar 28 16:21:03 2020 No.11510051

>>11509998
the question isn't whether or not the 3's continue, that much is very obvious. the 3's continue. there indeed wont be a 4.

the question is what does "infinite" mean?
>arrive at an infinite decimal number expansion in a finite time
i feel the wording of this assumes "infinity" is reachable.

it's one thing to say the 3's continue.
it's another thing to say the 3's continue decisively further than unimaginably long, which is what "infinitely" means to me. Saying it with such defacto certainty makes it seem like an infinity has already been achieved in whole during the course of human history and has been bounded, contained, and conveniently packaged in a nice little concept that can be as easily or discretely understood as the integer "1" without ambiguity, and because it has such a similar packaging it must therefore be allowed to be used similarly as discrete integers.

>>	Anonymous Sat Mar 28 16:26:26 2020 No.11510070 >>11508806 wtf is this? lol schizo

Anonymous Sat Mar 28 16:46:25 2020 No.11510125

>>11510020
>"0.333..." is 'trying it's darndest to reach 1/3',
This wording would suggest a process. But 0.333... is not a process. It is a number.

> the emergent property of there being unending 3's
Ok, but all the 3's are all there without the need to proces each of them.

>means it never actually reaches 1/3.
It doesn't "reach", because again, it is not a process. It doesn't follow from this that "0.333... is not 1/3".

In fact it turns out that 0.333... is 1/3. How?
By recognizing that 0.333... is the limit of the infinite sequence of numbers 0.3, 0.33, 0.333, ...
The number 0.333... is not in this sequence, nor does the sequence ever reach 0.333... None the less, 0.333... is the limit of the sequence.
It can also be shown through analysis, that 1/3 is also the limit of the sequence. Therefor we
conclude that 1/3 = 0.333...

Anonymous Sat Mar 28 16:59:44 2020 No.11510170

>>11510125
So you cannot pin a number amount on the amount of 3's in "0.333...", arrive at some arbitrary conclusion that "0.333..." is a simple-as decimal number which plainly just exists as discernibly as any integer might, and that this decimal number "0.333..." explicitly equals the fraction 1/3, just because you're confusing limit with equality?

1/3 is the limit of what "0.333..." is... well, not TRYING to reach because you don't hive with that vocabulary... so..
1/3 is the limit of what "0.333..." ... is?
Is that what you're saying?
(0.333...)'s limit is (0.333...)
...
???

Anonymous Sat Mar 28 17:06:27 2020 No.11510185

>>11510051
>makes it seem like an infinity has already been achieved
Well, yes. We could say that infinity has been achieved.
When we write 0.333..., that is a finite notational convention to refer to a zero followed by a decimal point and them infinitely many threes. We have a finite way of writing something infinite. We do not need to process or reach each 3. Simply by definition of the notation, we know that all the 3's are there, each in their right place. As such, one you say that we have "achieved infinity". But then again, i wouldn't say "achieved" because as I keep saying, we are not dealing with a process.

>>	Anonymous Sat Mar 28 17:07:18 2020 No.11510187 >>11510170 what 0.333 IS NOT: a process a measurement what 0.333... IS: a number, i.e. a definite point on the number line

>>	Anonymous Sat Mar 28 17:11:39 2020 No.11510206 >>11510170 Let S be the infinite sequence (0.3, 0.33, 0.333, ...) The limit of S is 1/3 The limit of S is 0.333... 1/3 is 0.333...

Anonymous Sat Mar 28 17:14:03 2020 No.11510216

>>11510125
I think your issue is that you're still clinging to the idea that 1/3 = 0.333... even though a simple proof was provided via division steps.
>1/3 > 0.3
>1/3 > 0.33
>1/3 > 0.333
>assume any continuation of this process results in the ever-continuing process of:
>1/3 > 0.333...
it holds true for any and all continuities of 0.333...'s expansion, and that is what both "infinity" and the "..." notation accomodate or imply.
Continuation.

Alternatively, using your notation:
> 1/3 > [0.3]
> 1/3 > [0.3, 0.33]
> 1/3 > [0.3, 0.33, 0.333]
> ...
> 1/3 > [0.3, 0.33, 0.333, ...]

Anonymous Sat Mar 28 17:24:27 2020 No.11510248

>>11510206
>The limit of S is 1/3
>The limit of S is 0.333...
Each of these statements inherently invalidates the other. Only one can be true. Technically the second one isn't true at all cause you appear to be assuming 0.333... has n-discernible difference over a real number n amount of 3's appearing incrementally in each element if the set defining the sequence.
In essence, what you're saying is [0.3(n+1 amount of 3's) is the limit of 0.3(n amount of 3's), which
>1. is stupid
and
>2. defies your assumption of (0.333...)'s discrete behaviour, which it can't very well be discrete if it's constantly changing. The integer 1 never changes into another number, nor does it's size change.

Anonymous Sat Mar 28 17:27:59 2020 No.11510261

>>11510216
This was false the two previous times you posted it, and it keeps being false.

>it holds true for any and all continuities of 0.333...'s expansion
No it doesn't. It only holds true for any and all FINITE "continuities of 0.333...'s expansion"

Anonymous Sat Mar 28 17:37:38 2020 No.11510285

>>11510248
>Only one can be true
Which would make them both the same statement. Which means the 1/3 is 0.333...

>[0.3(n+1 amount of 3's)] is the limit of 0.3(n amount of 3's)
No, that's not how limits work.
[0.3(n amount of 3's)] is the limit of 0.3(n amount of 3's)

(this is sort of a weird notation for limits and sequences you've invented here, but i'm trying to work with it)

Anonymous Sat Mar 28 17:38:42 2020 No.11510288

>>11510170
the definition of 1/3 is:
divide [0,1] into three parts of the same length. this number is the left end point of the second part.

the definition if 0.333... is:
this number lies in [0,1]
this number lies in [3/10,4/10]
this number lies in [33/100,34/100]
this number lies in [333/1000,334/1000]
this number lies in [3333/10000,3334/10000]
...

this is literally the definition of decimal expansion

Anonymous Sat Mar 28 17:41:25 2020 No.11510300

>>11510261
ALL EXPANSIONS OF 0.333... ARE FINITE
ANY
ALL
EVERY
WHY?
BECAUSE INFINITY IS DEFINED BY THE FINITE >>11508995

" A L L " values within the INFINITE set are FINITE, and sequencing THROUGH " A L L " values of the infinite set is what DEFINES infinity.
However "ALL" elements of an un-numbered length set returns NO KNOWABLE NUMBER to represent the AMOUNT OF ELEMENTS in the set. Infinity represents it, but infinity is an adjective, an adverb, not a noun, and definitely not a NUMBER.

this does not mean "continue using '...' notation and just fuck around"
It means STOP FUCKING USING "..." NOTATION CAUSE IT DOESN'T MEAN ANYTHING.

IF YOU DON'T TEST HOW MANY 3'S THERE ARE, THERE ARE JUST AS LIKELY TO BE ONLY 1.
0.3

IF YOU TEST HOW MANY 3'S THERE ARE, YOU MAKE AN OBSERVATION TO AN ARBITRARY FINITE DEGREE BOUND WITHIN THE SET OF INTEGERS, WHICH IS AN ARBITRARY FINITE NUMBER.
A NUMBER WHICH WILL NOT BE PREDESTINED FOR YOU, BUT A NUMBER WHICH YOU MUST PROVIDE, FOR IT MUST BE A REAL NUMBER AMOUNT OF 3'S BECAUSE INFINITY IS NOT A NUMBER AMOUNT AND FAILING TO TEST ASSUMES ONLY ONE 3.
0.3
don't use [math]0.333\dots[/math]
use [math]0.333\dots_{x=n}[/math] to determine the degree of your REQUIRED DECIMAL ACCURACY LIMIT.

Anonymous Sat Mar 28 17:43:42 2020 No.11510306

>>11510248
a sequence can have at most 1 limit
if you know that the limit of this sequence is some real number A
and if you know that the limit of this sequence is some real number B
the only logical conclusion is that A = B

this is how math actually works how weird is that

>>	Anonymous Sat Mar 28 17:45:21 2020 No.11510309 I need 33 decimals of accuracy on 1/3 >[math]\frac{1}{3} > 0.333..._{x=33}[/math] simple as.

>>	Anonymous Sat Mar 28 17:49:15 2020 No.11510321 >>11510300 >ALL EXPANSIONS OF 0.333... ARE FINITE The expansion of 0.333... is infinite 0.3 finite 0.33 finite 0.33333333333333333333333 finite 0.333... infinite See how that works?

>>	Anonymous Sat Mar 28 17:51:38 2020 No.11510326 >>11510300 >It means STOP FUCKING USING "..." NOTATION CAUSE IT DOESN'T MEAN ANYTHING. "..." in 0.333... means that the n-th digit is 3 for all n

>>	Anonymous Sat Mar 28 17:52:35 2020 No.11510327 >>11510300 >FOR IT MUST BE A REAL NUMBER AMOUNT OF 3'S No it doesn't. It's an INFINITE DECIMAL EXPANSION. By the very definition of INFINITE DECIMAL EXPANSION it can not have a real number amount of 3's. That's what INFINITE DECIMAL EXPANSION means.

Anonymous Sat Mar 28 17:56:05 2020 No.11510335

>>11510321
sequencing through the set of all integers is an infinite process.

0.333... does not contain "infinite 3's"
0.333... contains an arbitrary finite amount of 3's that you're willing to work with and compute upon.
0.3 + 0.3 = 0.6
0.33 + 0.33 = 0.66
0.333 + 0.333 = 0.666
0.3333 + 0.3333 = 0.6666
>if "0.333..." truly contains infinite 3's
>then:
0.333... □ □ □
well shit i'm trying to add another "0.333..." after it but I can't even make it to the addition sign because i have to spend the rest of fucking forever writing out more 3's so i can actually accurately do real fucking math on actual digits and not just made-up math on retarded assumptions of ignorance!

Anonymous Sat Mar 28 18:08:33 2020 No.11510368

>>11510335
I'm not even sure you're the same anon I began this discussion with.

>0.333... does not contain "infinite 3's"
Yes it does. It does by definition of the notation.

>well shit i'm trying to add another "0.333..." after it
well shit i'm trying to add another "0.333..." after it but I can't even make it to the addition sign
You just write 0.333... + 0.333... That's the whole point of the ... elipsis notation: to not having to spend the rest of fucking forever writing 3's.

Decimal expansion is just a notation for refering to a number. It doesn't change the number's place on the number line. The number still follows all the usual arithemtic laws.

>>	Anonymous Sat Mar 28 18:09:36 2020 No.11510373 >>11510335 >>11510368 As it turns out: 0.333... + 0.333... = 0.666...

Anonymous Sat Mar 28 18:13:37 2020 No.11510393

[math]\frac{1}{3} > 0.333... \\ \\ 3(\frac{1}{3}) > 3(0.333...) \\ \\ \frac{3}{3} > 0.999...[/math]
>1/3 > 0.333...
>...
>1/3 > 0.3333
>1/3 > 0.333
>1/3 > 0.33
>1/3 > 0.3
T R U E
ALL CHECKS OUT!

[math]\frac{1}{3} = 0.333... \\ \\ 3(\frac{1}{3}) = 3(0.333...) \\ \\ \frac{3}{3} = 0.999...[/math]
>1/3 = 0.333...
>...
>1/3 = 0.3333
>1/3 = 0.333
>1/3 = 0.33
>1/3 = 0.3
F A L S E
ITS ALL WRONG

>>	Anonymous Sat Mar 28 18:14:52 2020 No.11510398 >>11510393 This is nonsense.

>>	Anonymous Sat Mar 28 18:17:02 2020 No.11510407 >>11508439 Prove it wrong, faggot. Find a number strictly inbetween 1 and .999... The reals are dense, therefore there should be an INFINITE number of numbers for you to use. Pick one and show me, or shut your retarded ass up.

>>	Anonymous Sat Mar 28 18:18:02 2020 No.11510409 >>11510398 "..." means "continued" shocker, i know.

>>	Anonymous Sat Mar 28 18:18:05 2020 No.11510410 >>11508439 >You're really proud of this image and constantly repost Imagine being stupid enough to believe that /sci/ is one person. You don't, but others might have to.

>>	Anonymous Sat Mar 28 18:19:06 2020 No.11510412 >>11508444 Autism =/= wrong. The image is, potentially, proof of that.

>>	Anonymous Sat Mar 28 18:20:12 2020 No.11510420 >>11508466 Retard, he said it RESULTS in contradictions. He did NOT say that it IS a contradiction. Learn to read, faggot.

>>	Anonymous Sat Mar 28 18:20:58 2020 No.11510424 >>11510410 Surely no one else but the retarded author would care enough to name an image that is also full of easily disproveable retard tests which only the author could believe in.

>>	Anonymous Sat Mar 28 18:21:15 2020 No.11510426 >>11508448 You are fully within your rights to make an image with objectively wrong information. I would strongly suggest you not do that, but you can.

>>	Anonymous Sat Mar 28 18:22:16 2020 No.11510431 >>11509455 >Real numbers are literally the same as geometric constructs. Fucking kill me.

>>	Anonymous Sat Mar 28 18:24:15 2020 No.11510437 >>11509811 >1/3 always is represented by some irrational repeating number. What definition of "irrational" are you using? I ask because you're clearly not using a definition that people who actually understand math use.

>>	Anonymous Sat Mar 28 18:26:31 2020 No.11510448 >>11510393 What does 1/3 equal in decimal notation according to your retard logic?

Anonymous Sat Mar 28 18:27:55 2020 No.11510454

>>11510409
Usually 'continued' in this context means continued infinitely.

If you refuse to accept that and keep insisting that is means continoued with a finite amount of 3s, then we need another notation that you can accept for the concept on infinite decimal expansion, so we can at least discuss the same topic.

>>	Anonymous Sat Mar 28 18:31:21 2020 No.11510464 >>11510424 Then fucking disprove it if it's so easy.

Anonymous Sat Mar 28 18:33:47 2020 No.11510472

>>11510437
Irrational is inequal.
Pi is equal to a decimal number that has not been fully discovered, such that the decimal evaluation of pi must therefore be strictly less than the "number" [math]\pi[/math]
3 < pi
3.14 < pi
3.141 < pi
3.1415 < pi
this continues forever for all discoverable decimal digits of evaluating pi

property of irrationality.
0.3 < 1/3
0.33 < 1/3
0.333 < 1/3
0.3333 < 1/3
This continues forever for all discoverable decimal digits of evaluating 1/3

>>	Anonymous Sat Mar 28 18:34:33 2020 No.11510479 >>11510448 It wouldn't have one, according to anon, I think.

>>	Anonymous Sat Mar 28 18:36:02 2020 No.11510484 >>11510472 >Pi is equal to a decimal number that has not been fully discovered how many digits does this decimal number have ?

>>	Anonymous Sat Mar 28 18:37:11 2020 No.11510487 >>11510472 Stop making up and misusing mathematical terminology.

>>	Anonymous Sat Mar 28 18:39:55 2020 No.11510499 >>11510472 Why are you lying by implying that you know what you're talking about?

>>	Anonymous Sat Mar 28 18:40:25 2020 No.11510500 >>11510487 Eat shit nigger retard, irrationality has other elements but unending expanding decimal is literally one of the defining features.

>>	Anonymous Sat Mar 28 18:43:27 2020 No.11510509 >>11510500 >Irrational is inequal. That's the misusing part, you idiot.

Anonymous Sat Mar 28 18:43:50 2020 No.11510511

>>11510472
I have no illusions of changing you mind, but you should know that your definiton does not agree with the usual definiton of irrational number, that most everyone else uses.

An irrational number is on that can not be written as a fraction p/q, where p and q are integers.

Pi, the ratio between a the area of a circle and the square of the radius of the same circle, is irrational.

3.1415 can be written 31415/10000 and so is rational.

0.3 = 3/10 is rational
0.33 = 33/100 is rational

1/3 is rational

>>	Anonymous Sat Mar 28 18:44:39 2020 No.11510515 >>11510472 and since the pattern continues, by your logic 3 < pi 3.14 < pi 3.141 < pi 3.1415 < pi .. pi < pi

Anonymous Sat Mar 28 18:48:10 2020 No.11510527

>>11510509
Defining where the decimal place at which the irrational expanding decimal suddenly equals the value of it's limit is your burden to prove, if you feel that way.
Pi > 3
Pi > 3.1
Pi > 3.14
How many decimal digits are needed to equate pi?
Reminder: infinity is not a number amount, because it isn't even a number

:p

You telling me you never thought about this shit even once in your fucking life?

>>	Anonymous Sat Mar 28 18:51:08 2020 No.11510534 >>11510515 Nigga even all 50 trillion known decimal digits of pi still aren't there. You gonna pretend to know more than the ones that have been discovered? You got a 10% chance of guessing the immediately next digit correctly, go for it fag.

>>	Anonymous Sat Mar 28 18:55:13 2020 No.11510551 >>11510534 completely irrelevant. explain how is 0.3 < 1/3 0.33 < 1/3 0.333 < 1/3 .. 0.333... < 1/3 different from 3 < pi 3.14 < pi 3.141 < pi 3.1415 < pi .. pi < pi

>>	Anonymous Sat Mar 28 18:57:06 2020 No.11510560 >>11510527 Don't change the subject, subhuman. We are talking about your objectively WRONG definition of irrational. We need to clear up you not knowing BASIC mathematical terminology before we can get to anything proof related.

>>	Anonymous Sat Mar 28 18:57:34 2020 No.11510562 >>11510551 All the digits of 0.333... are known?

Anonymous Sat Mar 28 18:58:18 2020 No.11510566

>>11510551
That would require explaining to you how much of a retard you are for thinking infinity is something which exists or is applicable to knowing "infinite" digits of pi.

You can read the rest of the thread for that, i've already shown it dozens of times.

>>	Anonymous Sat Mar 28 18:59:13 2020 No.11510571 >>11510562 Yes. It doesn't matter what n is, the nth decimal will be 3. So yes they are all known, even if we haven't "discovered" them yet.

>>	Anonymous Sat Mar 28 19:00:27 2020 No.11510579 >>11510566 Infinity does exist mathematically. Stop being a mathematical version of a creationist.

>>	Anonymous Sat Mar 28 19:01:38 2020 No.11510584 >>11510571 n'th decimal = real number decimal, just make sure to remember that part too.

Anonymous Sat Mar 28 19:02:16 2020 No.11510585

>>11510566
>That would require explaining to you how much of a retard you are for thinking infinity is something which exists or is applicable to knowing "infinite" digits of pi.
I don't need to invoke infinity at all to define 0.333... or a decimal expansion of pi.
>You can read the rest of the thread for that, i've already shown it dozens of times.
you haven't shown nothing, all your claims are getting disproved over and over

>>	Anonymous Sat Mar 28 19:02:50 2020 No.11510590 >>11510579 Ironic when you treat infinity as infalliable as a creationist treats the bible, you utter cumstain retarded hypocrite of a failed experiment.

>>	Anonymous Sat Mar 28 19:06:37 2020 No.11510600 >>11510571 This is completely retarded, FYI.

>>	Anonymous Sat Mar 28 19:06:58 2020 No.11510605 >"infinity exist!" >prove it >"no proof needed, its unfalsifiable XD" >"god exist!" >prove it >"no proof needed, its unfalsifiable XD" [math]I R O N Y[/math]

>>	Anonymous Sat Mar 28 19:08:08 2020 No.11510610 >>11510590 Infinity does exist because, just LITERALLY EVERYTHING ELSE IN MODERN MATH, we defined it using an axiomatic system.

>>	Anonymous Sat Mar 28 19:09:11 2020 No.11510615 >>11510600 Enlighten me, what is the nth digit if not 3?

>>	Anonymous Sat Mar 28 19:09:33 2020 No.11510617 >>11510610 axiom of infinity is LITERALLY a joke you penis head.

>>	Anonymous Sat Mar 28 19:09:52 2020 No.11510618 >>11510585 >I don't need to invoke infinity at all to define 0.333... or a decimal expansion of pi. Technically you do. Any finite decimal expansion will not be pi.

>>	Anonymous Sat Mar 28 19:12:21 2020 No.11510630 >>11510617 1) Stop misusing literally. 2) Prove it. Prove it's a "joke". Find an actual contradiction instead of whining about how it "doesn't exist".

>>	Anonymous Sat Mar 28 19:13:15 2020 No.11510633 >>11510615 The retarded bit your definition of irrational, that you think this question is relevant.

>>	Anonymous Sat Mar 28 19:13:42 2020 No.11510634 >>11510605 Your dishonest comparison is not appreciated. Infinity exists because we defined it, and it doesn't lead to contradictions.

>>	Anonymous Sat Mar 28 19:17:43 2020 No.11510642 >>11510618 technically all I need is the universal quantifier I don't need to actually carry out an infinite process

>>	Anonymous Sat Mar 28 19:19:28 2020 No.11510650 >>11510633 >The retarded bit your definition of irrational, that you think this question is relevant. "what is the n-th digit" is actually the only relevant question regarding decimal expansions lmao

>>	Anonymous Sat Mar 28 19:22:22 2020 No.11510654 >>11510633 Don't dodge the question. What is it?

Anonymous Sat Mar 28 19:25:37 2020 No.11510663

>>11510630
axiom of infinity allows for 1 infinity to exist, and that infinity is describing the size of the set of all natural numbers.
I constructed this set in >>11508995 and sourced a /sci/ trusted go-to to insure infinity is not a number, which makes it's application to the size of the set of "all" numbers functionally identical to the word "unlimited".

The greater issue exists with the assumption of whether or not "unlimited real numbers" do in fact exist.
If humanity was destroyes by a meteor, who'd be around to continue counting?
Whatever largest real number that had been instantiated at that point would therefore in fact be the last number, and the amount of number usage would no longer increase.

If you don't like the philosophical angle, whatever. It's not even required.

Anonymous Sat Mar 28 19:26:01 2020 No.11510664

>>11510642
You still can't consider infinite decimal expansions without invoking infiniti. The concept infinity is inherent in the concept infinite decimal expansion.

>>11510650
No. The decimal expansion of pi has been show to be infinite without anyone knowing the n:th digit for every n.

>>	Anonymous Sat Mar 28 19:29:10 2020 No.11510670 >>11510663 >axiom of infinity allows for 1 infinity to exist, Well, that's a shitty axiom since the infinity of the reals is known to be greater than the infinity of the naturals.

Anonymous Sat Mar 28 19:30:07 2020 No.11510674

>>11510634
>god created us and we created infinity(god)
>chicken created the egg which then hatched into the chicken which laid it
>not a contradiction
infinity's definitions and usages are so laughably contradicting that it seems like an inescapable law of the universe that it can't actually exist.
You are so, so wrong.

>>	Anonymous Sat Mar 28 19:35:46 2020 No.11510680 >>11510663 And from that axiom we proved that there exists more infinities than just the one explicitly defined.

>>	Anonymous Sat Mar 28 19:36:22 2020 No.11510683 >>11510674 >infinity's definitions and usages are so laughably contradicting give one example

>>	Anonymous Sat Mar 28 19:37:59 2020 No.11510689 >>11508995 >contain them between and opening and closing bracket, defying the definition of infinity being "unbounded". You are retarded.

>>	Anonymous Sat Mar 28 19:40:53 2020 No.11510695 >>11510674 >infinity's definitions and usages are so laughably contradicting also do you consider quantifying over natural numbers as usage of infinity? because that's all you need to define, say, decimal expansions and limits

>>	Anonymous Sat Mar 28 19:43:33 2020 No.11510706 >>11510674 FUCKING PROVE IT! If it's so easy and laughable, then it should be easy for a "genius" like you to find one. Do it. Do it now. Don't change the subject, just do it now.

Anonymous Sat Mar 28 19:45:23 2020 No.11510710

>>11510634
https://www.wolframalpha.com/input/?i=infinity
>Infinity is an unbounded quantity greater than every real (and every whole) number.
https://www.wolframalpha.com/input/?i=quantity
>a Quantity is how much there is or how many there are of something that you can quantify
https://www.wolframalpha.com/input/?i=quantify
>to Quantify is to express as a number or measure or quantity
https://www.wolframalpha.com/input/?i=is+infinity+a+number%3F
>∞ is not a number
https://www.wolframalpha.com/input/?i=Does+1%2F%28not+a+number%29+%3D+1%2Finfinity%3F

circular, contradicting, utterly retarded.
thanks infinity.

>>	Anonymous Sat Mar 28 19:47:47 2020 No.11510722 >>11510689 learn what boundaries are, autismo. I mean it in more than one way.

>>	Anonymous Sat Mar 28 19:49:03 2020 No.11510727 >>11510710 >circular, contradicting, utterly retarded. give one example

>>	Anonymous Sat Mar 28 19:50:16 2020 No.11510732 >>11510727 the whole post one example. There are 1 more in this thread. Digest glass, [math]senpai[/math]

>>	Anonymous Sat Mar 28 19:52:20 2020 No.11510738 >>11510710 >https://www.wolframalpha.com/input/?i=Does+1%2F%28not+a+number%29+%3D+1%2Finfinity%3F It literally says the exact opposite of what you claim it says, lying retard.

>>	Anonymous Sat Mar 28 19:53:55 2020 No.11510743 >>11510732 https://www.wolframalpha.com/input/?i=Does+%28not+a+number%29+%3D+infinity%3F Lying retard. It literally says that "not a number" is not the same as "infinity".

>>	Anonymous Sat Mar 28 19:54:15 2020 No.11510744 >>11510722 I think you should learn what mathematics is. You don't seem to have a single clue.

>>	Anonymous Sat Mar 28 19:57:16 2020 No.11510754 File: 165 KB, 800x800, 1524043147486.jpg [View same] [iqdb] [saucenao] [google] >>11510738 >is ∞ a number? >>no >is "1/(not a number) = 1/∞" true? >>no goddamnit you fuck

>>	Anonymous Sat Mar 28 20:06:15 2020 No.11510771 >>11510754 I hope you never try to learn javascript.

Anonymous Sat Mar 28 20:08:32 2020 No.11510778

>>11510743
It says infinity is not a number

therefore infinity = (not a number)

1/(NaN) = some bullshit irreducible letter-a symbol, may as well be undefined. Doesn't do jack shit.

but 1/infinity = 0
they should have the same result, both aren't numbers.
https://www.wolframalpha.com/input/?i=%281%29+divided+by+%28potato%29

says infinity isn't a number, but treats it as number for arithmatic. says it isn't a number, but defines it as a quantity, where quantites are defined by numbers.

Anonymous Sat Mar 28 20:19:04 2020 No.11510803

>>11510754
>>11510778
You are either lying or so stupid that I can't comprehend it. The link does NOT say "Is infinity a number". What the fuck is happening? It says "is infinity equivalent to "not a number"" and it answers "false". It literally says the exact opposite of what you say it does, but you are so stupid that you can't understand how double negatives work. Knowing how to work with double negatives is below Jr. High algebra level math. How the fuck did you not understand this? I'm completely shook.

>>	Anonymous Sat Mar 28 20:22:23 2020 No.11510812 >>11510803 >but you are so stupid that you can't understand how double negatives work. Maybe they're Polish?

>>	Anonymous Sat Mar 28 20:41:27 2020 No.11510857 >>11510803 there are multiple links in that post, coombrain anon.

>>	Anonymous Sat Mar 28 23:26:28 2020 No.11511153 >>11510664 https://mathworld.wolfram.com/PiDigits.html formula (3) A recursive formula, conjectured to give the nth hexadecimal digit of pi-3

>>	Anonymous Sat Mar 28 23:45:11 2020 No.11511196 >>11511153 [math] \boxed{ \text {nth hexadecimal of} ~ \pi -3} \\ x_0=0\\ x_n= \text{frac} \left ( 16x_{n-1}+\frac{120n^2-89n+16}{512n^4-1024n^3+712n^2-206n-21} \right ) \\ d_n=\left \lfloor 16 x_n\right \rfloor [/math]

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/sci/ - Science & Math