/sci/ - Science & Math

[Anonymous No.10982184]

Okay so this is bugging me
1 ÷ 3 = .333- (one third)
But
.333- × 3 = .999

3/3rds is less than one according to our math?

[Anonymous No.10982191]

>>10982184
.999(infinite 9) = 1

[Anonymous No.10982219]

>>10982184
Lmao, you should work on your bait quality

[Anonymous No.10982222]

>>10982184
Metric bullcrap

[Anonymous No.10982227]

>>10982184
Here you go senpai:
[math]
\sum_{k=1}^{\infty} 9(1/10)^k = \frac{0.9}{1-0.1}
\\
\sum_{k=1}^{\infty} 9(1/10)^k = \frac{0.9}{0.9}
\\
\sum_{k=1}^{\infty} 9(1/10)^k = 1
\\
0.9+0.09+0.009+... = 1
\\
\therefore 0.999... = 1
[/math]

[Anonymous No.10982393]

>>10982184
".99999..." and "1" are two notational representations of the same number under the standard construction of the reals

[Anonymous No.10982430]

>>10982393
So you believe that If a number has nothing between it and another number then it's the same number? Seems like special pleading.

[Anonymous No.10982453]

No. .999... is not one. If it were, line AZ and BZ would have the same slope, (paralel) yet somehow converge at Z.

[Anonymous No.10982455]

>>10982184
No. .999... is not one. If it were, line AZ and BZ would have the same slope, (paralel) yet somehow converge at Z.

[Anonymous No.10982466]

>>10982455
I reject your hypothesis

[Anonymous No.10982481]

>>10982430
He's just telling it like it is.

[Anonymous No.10982486]

>>10982455
geometric proofs are notoriously weak when dealing with infinity:

distance =/= length

hypotenuse length, [math] n \rightarrow \infty [/math]

a+b or [math] \sqrt{a^{2}+b^{2}} [/math] ?

[Anonymous No.10982618]

>>10982486

That is kind of the same as this. They are good examples of why you can't assume that a process taken to infinity equals it's limit. A staircase with infinitely many steps of infinitely small size is not a line. A polygon with infinitely many right angles is not a circle. A number with infinitely many trailing nines is not the next digit up.

[Anonymous No.10982658]

>>10982455
is this a wildburger thing? never saw someone try so hard at being wrong

[Anonymous No.10982695]

>>10982658

Insults = I can't find anything wrong with your logic.

[Anonymous No.10982697]

>>10982695
no i'm not trying to use an insult, "wildburger" is a reference to N J Wildberger, not an amerifat thing

[Anonymous No.10982725]

>>10982184
As the decimal place approaches infinity the difference between .999999999 and 1 becomes so infinitesimally small that .9999999 = 1

[Anonymous No.10982754]

>>10982184
.999... = 1
brainlet

[Anonymous No.10982769]

>>10982618
>They are good examples of why you can't assume that a process taken to infinity equals it's limit.
It is, you don't understand what a limit is.

[Anonymous No.10983056]

>>10982769
>It is, you don't understand what a limit is.
> Doesn't bother to try to explain anything.

These discussions turn into religion really quickly. If a number with infinite digits is a valid construct, then why isn't a staircase with infinite steps?

[Anonymous No.10983123]

>>10983056
>turn into religion really quickly. If
google it, wikipedia it - no-one here is your mommy

[Anonymous No.10983136]

>>10982430
That's literally true, calling it "special pleading" doesn't mean anything.

[Anonymous No.10983141]

>>10982430
You're just saying that if x-y=0 then x=y, which is trivially true.

[Anonymous No.10983142]

>>10983136

So if there is nothing between A and B, then A and B are the same letter?

[Anonymous No.10983149]

>>10983142
in R they are

[Anonymous No.10983161]

>>10983123

>I'm right, you're wrong. Google it, because I'm too lazy to defend myself.

[Anonymous No.10983218]

1/3 = 1/3
1/3 X 3 = 3/3 = 1
Decimals are fractions to the tenth power.
Everything I just typed is made up scribbles. This is why maths cant prove anything and is a great example. Could give a shit less about your "model" unless it provides more insights into a persuasive argument for a theory. But if the persuasive argument is squigglie math proofs fuck right off.

[Anonymous No.10983239]

>>10983056
>then why isn't a staircase with infinite steps?
It does not converge to a line. All you have to do is look at the definition a limit.

[Anonymous No.10983246]

> but muh .9's X infinity = 1

This is also retarded. 1 X infinity = Infinity
.9 X infinity means it can continue to be divided infinitely. Its a shitty system and maths is fucken gay

[Anonymous No.10983325]

>>10983161
ur not worth it

[Anonymous No.10983329]

>>10983246
x*inf=inf

[Anonymous No.10983338]

>>10983325
This dude has been checking this thread for over an hour just to say, "google it" and "you're not worth it"

kewl

[Anonymous No.10983628]

>>10983142
>what is a discrete space
brainlet.jpeg

[Anonymous No.10983630]

>>10983246
Nah you're just dumb

[Anonymous No.10985149]

>>10982430
I don't "believe" anything about the statement I made. It's a definite, provable fact about the standard construction of the reals and how that relates to our symbolic language for notating elements of the reals.

[Anonymous No.10985176]

1/3 isn't equal to 0.333, 0.333 with the repeater symbol is an approximation of one third.
This is because you are in a reality where infinity is not defined, it's outside the dimension we inhabit.
So for example I can type 0.333..., or 0.333333333..., or with a million 3s, but I can't type infinite threes, so we use the symbol 1/3, or an approximation 0.333,
3 X 1/3 =1. 3 X 0.3333.. does not equal 1.

[Anonymous No.10985190]

>>10985176
>infinity is not defined
wew lad
Definition:
An unbounded quantity that is greater than every real number.

[Anonymous No.10985191]

>>10985176
1/3 = 3/10 + 1/30
= 0.3 + 1/30
= 0.33 + 1/300
= 0.333 + 1/3000
:
= 0.3... + 1/inf
= 0.3... + 0
= 0.3...

[Anonymous No.10985202]

:)
I don't mean it lacks a definition in the English language, I mean that you can't actually write an infinite number, you can only approximate, if you know what I mean,
This is confusing because we are taking approximations, running them through an equation, getting an answer that is intuitively incorrect.
It's just mixing up real world and vectored maths.

[Anonymous No.10985210]

>>10985202
>if you know what I mean,
not even a clue

[Anonymous No.10986319]

>>10982184
tell me when you reach that last digit

[Yuji Sakai No.10986335]

>>10985191
1/∞ ≠ 0

infinity is not a number, is a concept

[Anonymous No.10986453]

>>10982618
how is this invalid?

[Anonymous No.10986459]

>>10982184
>>10982191
>>10982219
>>10982222
>>10982227
>>10982393
>>10982430
>>10982455
>>10982481
>>10982486
>>10982618
>>10982658
>>10982695
>>10982697
>>10982725
>>10982754
>>10982769
>>10983056
>>10983123
>>10983136
>>10983141
>>10983142
>>10983149
>>10983161
>>10983218
>>10983239
>>10983246
>>10983325
>>10983329
>>10983338
>>10983628
>>10985149
>>10985176
>>10985190
>>10985191
>>10985202
>>10985210
>>10986319
>>10986335
>>10986453
1/3 is not .333 that is just an approximation, you can't represent 1/3 as a decimal but .333 repeating forever is the closest value because .334 is too big and .333 is slightly too small so when they show a repeating bar it is because .333 is not actually one-third but it is the closest you can get with decimal in base 10.

[Anonymous No.10986462]

>>10986453
because the infinite block has infinitely many deviations from the circular form.

[Anonymous No.10986463]

>>10985190
>quantity
>unbounded

[Anonymous No.10986484]

>>10986459
read a book

[Anonymous No.10986489]

>>10986484
>hurr infinite exists exist, just accept it
very enlightening

[Anonymous No.10986495]

>>10986335
sure bud
https://www.wolframalpha.com/input/?i=1%2Finf

[Anonymous No.10986502]

>>10986489
>exists exist
the best kind of exist

[Anonymous No.10986506]

>>10986495
>appeal to authority with no reasoning

[Anonymous No.10986516]

>>10986506
shitposter vs W|A, easy choice

[Anonymous No.10986524]

>>10986516
>I believe it but I can’t tell you why

[Anonymous No.10986529]

>>10986524
shitposter vs W|A, easy choice

[Anonymous No.10986532]

>>10986529

[Anonymous No.10986549]

>>10986462
>>10986463
>>10986484
>>10986489
>>10986495
>>10986502
>>10986506
>>10986516
>>10986524
>>10986529
>>10986532
.333 infinite times would have no value because infinity is not a number so an infinite number of 3s is also not a number

[Anonymous No.10986554]

>>10986549
>infinity is not a number
so what

[Anonymous No.10986564]

>>10986554
so .333 (infinite) cannot be a number either.

[Anonymous No.10986567]

>infinity is totally not a number you guys!
>”but what is it?”
>a quantity...

[Anonymous No.10986572]

>>10986564
yes, but the limit of the sequence .3, .33, .333, .3333,... surely can be defined as a number and that number is equivalent to 1/3

[Anonymous No.10986586]

>>10986572
in other words, 0.333... is limited by 1/3, and will never actually equal 1/3

[Anonymous No.10986592]

>>10986572
>>10986586
So .333... does not equal 1/3 and thus is not equivalent ?

[Anonymous No.10986595]

>>10986564
how exactly?

[Anonymous No.10986598]

>>10986592
0.333... is a meaningless expression. You’re assuming that something infinite exists. 0.333... should not be viewed as a number but it shows that as you repeat the process, 0.333... approaches 1/3. There’s no justification for treating it as a number though. Even if you did, it still can’t equal 1/3, because there is always a remainder.
0.33 is just as unequal as 0.333...
There is always a gap between them

[Anonymous No.10986622]

>>10986592
.3333.... IS grade school shorthand for "the limit of the sequence .3, .33, .333, .3333, ...". idk what the expression would mean otherwise. so, yes, .333.... is equivalent to 1/3

[Anonymous No.10986633]

>>10986598
this is not a good way to think about decimal representations. if you are going to think about decimals-as-real-numbers, you should think about all real numbers as equivalence classes of sequences.

the sequence implicitly represented by .3333.... is no less different from 1/3 as .999.... is in the equivalence class representing 1, or 1.99... is in the equivalence class representing 2.

[Anonymous No.10986652]

>>10982184
Anon it’s simple.
S=0.999...
10S=9.999...

10S =9.999...
-S =0.999...
9S= 9
S=1
0.999...=1

[Anonymous No.10986662]

>>10986652
>0.999... is a number
>you can multiply and add it
Yeah I’m gonna need a justification for your extension of arithmetical operations to infinite sums

[Anonymous No.10986681]

>>10986662
http://www-users.math.umn.edu/~kling202/hamline/calculus/Chapter2/Limits.pdf

literally done in any calc 1 class. changing the above argument from functions to sequences is trivial.

[Anonymous No.10986686]

>>10986681
>10S = 9.999...
Where is the ending 0?

[Anonymous No.10986689]

>>10986662
Finally someone who isn’t an idiot on this sub. Technically all numbers in decimal notation are infinitely long;
4 is really 4.0000...
You can also take the algebra a step further:
Since 1=0.999...
1=1
-0.999= -1
——————
0.000...1=0
Therefore all infinitesimals are equal to 0, since:
0.000...1*X = 0*X
0.000...X=0
except at x= infinity

[Anonymous No.10986705]

>>10986686
Are you fucking stupid.
It’s non terminating

[Anonymous No.10986727]

>>10986705
Then how do you justify multiplying it? Where is the rule that says we can multiply an infinite sum? I certainly cannot prove such a thing empirically or even intuitively. You’re pulling these rules out of nowhere. That’s not how mathematics works

[Anonymous No.10986747]

>>10986727
Anon, every mathematician in the world disagrees with you.
Why do we allow people who haven't even done Calc to make math threads.

[Anonymous No.10986752]

>>10986747
And yet you yourself cannot give a justification. You’re blindly believing “every mathematician in the world” and it’s embarrassing. If you judged mathematics by majority and authority, then at one point, you would have detested infinity and infinitesimals

[Anonymous No.10986758]

>>10986727
>You’re pulling these rules out of nowhere. That’s not how mathematics works
Except that's exactly how mathematics works. It's the study of games we play on abstract structures.

[Anonymous No.10986769]

>>10986752
Yes anon, you, who clearly have no mathematical training whatsoever, are in the right here. A breakthrough thinker, no one has ever questioned this before and you are going to change the field of mathematics with this.

[Anonymous No.10986787]

>>10986662
Do you also reject multiplying pi by 2?

[Anonymous No.10986790]

>>10986622
oh ok

[Anonymous No.10987133]

>>10986727
>Where is the rule that says we can
Where is the rule that says we can't

[Anonymous No.10988357]

bump

[Anonymous No.10988381]

>>10983142
Yes, that's literally how you prove uniqueness

[Anonymous No.10988448]

1/3 is not strictly equal to 0.333...
instead, it cannot be strictly equal in decimal notation. We're taught that anything can be rendered in decimal, but for some things it's not really accurate and is simply more of a cheat.

unfortunately the cheat also works towards convincing some people that 0.999... = 1, even though this is not essentially the case. This has to do with seemingly-infinite repetition. In the case of rendering 1/3 as 0.333... using the cheat, it makes enough sense that this specific rendering of 0.333... approximating 1/3 specifically, times 3, would produce 0.999..., and that 1/3 *3 = 1.
however, this does not hold true for something like
[math]\sum_{n}^{\infty}\frac{1}{2^n}[/math] which intends to strictly produce a 0.999... result. This calculus however "uses" "infinity", which rationally isn't actual infinity but is instead seemingly infinite.

to quickly define the difference between infinite and seemingly-infinite, both are technically shortened from their results and there is an unimaginable degree of accuracy should one continue with calculation, so "seemingly-infinite" is more like a realnumber (infinity-1). There is no countable proof for either infinity or seemingly-infinite, so in the same regard there is no strong evidence an (infinity-1) cannot exist as a real number too long to intelligently do any math with, which would give it the same relevant property as straight-up "infinity" does. In all, anything that is described as infinite is more likely than not simply seemingly-infinite.

[Anonymous No.10988458]

>>10988448
This seemingly-infinite term is necessary for describing the 0.999... number produced by the above sum algorithm, because it is strictly provable to not be the same 0.999... number rendered from 0.333...*3 where we got the 0.333... from 1/3 specifically. Any partial sum step of [math]n[/math] within the sum will produce a string of 9's followed by a string of various digits. The infinity-hopefuls contest that those trailing digits would simply vanish under the condition that actual infinity had been reached from numerating [math]n\rightarrow\infty[/math], but since there is no way to actually do this, this vanishing cheat isn't real either. The true result of this sum is a seemingly-infinite string of 9's, followed by a seemingly-infinite string of various digits, which is different from the 0.333...*3 = 0.999... number which is solely just a seemingly-infinite string of 9's.

a lot of mental cheating occurs when rendering repeating numbers in higher maths, and for this example we end up shortening what seems to be infinitely repeating patterns down to just 3 digits followed by an ellipses rendered as [math]0.999...[/math]

[Anonymous No.10988513]

>>10988458
[math]
1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}
[/math]

[Anonymous No.10988535]

>>10988513

[Anonymous No.10988601]

>>10988448
[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]

[Anonymous No.10988705]

>>10986453
A simple explanation is that infinity does not exist so you'll never have an actual circle.

[Anonymous No.10988714]

>>10988705
Perfect troll explanation.

[Anonymous No.10988737]

>>10986459
Thanks for quoting everyone in the thread. That was very helpful and not annoying at all.

[Anonymous No.10988748]

>>10988601
i hope there was a point to this post

[Anonymous No.10990466]

>>10988748
there is

[Anonymous No.10990727]

>>10982184
This is just a quirk of notation. 0.999... = 1. This is because what we mean by 0.999... is just the limit of 0.9 + 0.09 + 0.009 +...; and this limit is 1. This is trivial to see if you actually think of the definition of a limit for a series: The limit of a series a_i is c if for every epsilon > 0, there exists an N > 0, such that for all natural n >= N, the distance between a_n and c is smaller than epsilon. Or in short: The limit of a series is c if the series gets within any arbitrary distance of c eventually, which is obviously true for 0.999... and 1.

The reason it seems so illogical is that there seems to be some kind of room between 0.999... and 1; for any amount of nines there's still space between it and 1, so if you add nines forever, it will just get closer and never really there right? But there is no such thing as 'adding nines' as if it is some kind of temporal process. Thinking about it in these terms is already based on a misinterpretation of what 0.999... means.

[Anonymous No.10990738]

>>10988601
>p^n = 0
prove it

[Anonymous No.10990777]

>>10982219
Are you stupid?
0.999...=\=1 threads have been going strong for years...

[Anonymous No.10990785]

>>10986727
>You’re pulling these rules out of nowhere. That’s not how mathematics works
It LITERALLY is as any book on the foundations on mathematics will tell you.

[Anonymous No.10990823]

>>10990738
n=inf
done

[Anonymous No.10990847]

>>10986564
>>10986554

Wonder what the theological\metaphysical implication of the perfectly equal division of the one by the three not adding back to the one perfectly over an infinite series is. It's almost as if IsRaEl is somehow more than the sum of its parts somehow... Likely this is more due to the imprecise nature of finite math, but still an interesting thought.

[Anonymous No.10990850]

>>10990847
https://binged.it/2VbXfOf

[Anonymous No.10990855]

x = 0.999...
10x = 9.999...

10x - x = 9.999... - 0.999...
9x = 9
x = 1

0.999... = 1

[Anonymous No.10990862]

1/9 = 0.111...
+
8/9 = 0.888...
=
9/9 = 0.999...

[Anonymous No.10991492]

>>10990855
>>10990862
>>10988601
>>10988513
>>10986652
>>10982754
>>10982227
>>10982191
oh please continue, don't pay any attention to the fact that there are other people in the room.

[Anonymous No.10991504]

>>10990855
>10x = 9.999...
Where is the ending 0?
>>10990823
>n = inf
Still haven’t proven that n^inf is possible, let alone equal to 0

[Anonymous No.10991539]

[Anonymous No.10991680]

>>10982184
Why not live a carefree life in base 3?
[math]1_3\div10_3=0.1_3=\left({1\over{3^1}}\right)_{10}[/math]

[Anonymous No.10992148]

The thought just occured to me, Why would someone accept that 1/3 = 0.333... but not accept that 0.999... = 1.0 ?

[Anonymous No.10992151]

>>10992148
Because 1/3 isn’t equal to 0.333...

[Anonymous No.10992172]

>>10991680
>Why not live a carefree life in base 3?
I heard there's niggers in it

[Anonymous No.10992195]

Perhaps I sould be more specific. In the first post of this thread, Anon said he was "bugged" by the apparent paradox he posted. In that post, he accepted that 1/3=0.333... but did not acceept that 0.999...=1. That seems like cognitive dissonance, and something that should be pointed out, whether you believe in infintiy or not.

[Anonymous No.10992207]

>>10992195
With 0.999... we don’t see the “1” out front, so we might think they’re unequal. With 0.333... there doesn’t have to be a 1 there. We just assume it’s equal to 1/3. However, if we look at the fraction representations:
3/10, 33/100, 333/1000/ 3333/10000 etc.
we see how there’s always a remainder of 1. No matter how long the fraction is, there will always be a remainder. And just saying “go to infinity” doesn’t really justify how the remainder goes away.

[Anonymous No.10992214]

>>10992207
333...
——
100...

This is clearly not equal to 1/3

[Anonymous No.10992217]

>>10992214
0333...
———
1000...

fixed

[Anonymous No.10992249]

[math]\frac{1}{3} > \sum_{n=1}^{\infty}\frac{1}{3^n}[/math]

[Anonymous No.10992253]

[eqn]\frac{1}{3} > \sum_{n=1}^{\infty} \frac{1}{3^n}[/eqn]

[Anonymous No.10992586]

>>10991492
[math]
\boxed{0 < p < 1} \\
1 = p + (1-p) ~~~~~~ \overset{1}{ \overbrace{[=====p=====|==(1-p)==]}} \\
\text{divide p using x} ~~~~~~ \overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\
\\
\text{solve x and (p-x), when length ratios must be the same} \\
\dfrac{x}{p-x}= \dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow \underline{x=p^2} \Rightarrow \underline{(p-x)=p(1-p)} \\
\overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\
\\
\overset{1}{ \overbrace{ \underset{p^2}{[ \underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\
\overset{1}{ \overbrace{ \underset{p^3}{[ \underbrace{=====p^4=====|==p^3(1-p)==}]} ~~+ p^2(1-p)+p(1-p)+(1-p)}} \\
(1-p)+p(1-p)+p^2(1-p)+p^3(1-p)+ \cdots =1 ~~~~ \left | ~ \times \frac{1}{1-p} \right . \\
1+p+p^2+p^3+ \cdots = \dfrac{1}{1-p}
[/math]

[Anonymous No.10992594]

>>10991504
>>10986495

[Anonymous No.10992604]

>>10992586
You can’t justify the disappearance of the p^n term. Bullshit bullshit bullshit

[Anonymous No.10992616]

>>10992604
0<p<1

[Anonymous No.10992623]

>>10992604
disappearance?

[Anonymous No.10992632]

>>10992623
In the second to last line, the last term should be p^n, but instead there is (...). The last term gets smaller, but you haven’t proven that it becomes 0. The sum becomes arbitrarily close to 1, but it never equals 1.

[Anonymous No.10992664]

>>10992632
>>10986495

[Anonymous No.10992671]

>>10991539
Wait a minute with that brown example,
Like for real time out.

If you had 1 litre of water, so 1000 grams of water, and you pour it into 3 containers, you don't have 333.333... grams in each container, you have a precise weight in each container.
This analogy is rediculous, it's the same as saying 9=10,
You can't round up physical values.
If you buy a gram of coke, and the dealer taps it onto the scale until it's 0.9999999 grams, that isn't 1 gram.

This whole debate rages because of a misunderstanding between vectored maths and real world maths,
These symbols you are looking at are approximations done by humans in order to measure our world better, you cannot have an infinitely repeating number measured in the real world anymore than you can give a value in kilometres for how far away infinity is.

[Anonymous No.10992672]

>>10992664
Any non-zero number p multiplied by itself will not be equal to zero. So no matter what n value, p^n will never equal zero. It’s pure bullshit and you eat it up

[Anonymous No.10992682]

Theme of the thread:
https://youtu.be/MM62wjLrgmA

[Anonymous No.10992693]

what if i told you
>1/3 is NOT .333 ad infinitum

[Anonymous No.10992712]

>>10992693
heresy

[Anonymous No.10992752]

>>10992672
>>10986516

[Anonymous No.10992760]

>>10992752
and with that, you concede a lack of understanding. This discussion can go no further as you fail to defend your methods and have no chance of providing any reasons whatsoever for your sleight of hand trucks you call mathematics.

[Anonymous No.10992764]

>>10992760
the bus stop masturbator has spoken

[Anonymous No.10992876]

just convert your bases to something other than decimal. "0.333..." in decimal can be represented as 0.4 in duodecimal, which fits into 12 three times quite nicely.

[Anonymous No.10992880]

*which fits into 1(base 12), my bad

[Anonymous No.10993904]

bump

[Anonymous No.10994024]

some numbers shouldn't be rendered in decimal and should just be left as fractions, simple enough.

[math]1 \div 3 = \frac{1}{3} [/math]

[Anonymous No.10994045]

NO WOLFRAM WHAT ARE YOU DOING AAAAAAAAAAAAA

[Anonymous No.10994098]

>>10994045
>>10986529

[Anonymous No.10994107]

>>10994045
let's pretend finite is infinite

[Anonymous No.10994112]

>>10994024
1/3 = 0.1_3

[Anonymous No.10994119]

>>10986459
>mass quoting
use an approximation next time

[Anonymous No.10994120]

>>10986495
this should be undefined given inf/inf is undefined.

[Anonymous No.10994162]

>>10994120
sure bud

[Anonymous No.10994177]

>>10994162
glad you two agree now

[Anonymous No.10994199]

>>10994162
idk if you're being stupid or not but wolfram thinks 0.1 followed by 56 more 1's is the literal 1/9. wolfram is incredibly retarded.

[Anonymous No.10994393]

>>10994199
ok bubba

[Anonymous No.10994560]

>>10994199

[Anonymous No.10994581]

>>10982184
The limit of 9 times 1/10^n+1 as n approaches infinity is 1.

[Anonymous No.10994589]

>>10982455
You're taking a limit. 0.333... is an accident of notation.

[Anonymous No.10994595]

>>10994581
https://www.wolframalpha.com/input/?i=sum%5B1%2F10%5E%28n%2B1%29%2C%7Bn%2C1%2Cinfinity%7D%5D

infinity isn't a number btw.

[Anonymous No.10994598]

>>10983056
You need Jesus and to learn what a limit is.

[Anonymous No.10994600]

>>10982191
/thread

[Anonymous No.10994604]

>>10994598
limit is only a viable concept when using it with a number and not a retarded object like infinity, which by very definition is limitLESS.

>the limit is unlimited
please use your thinker.

[Anonymous No.10994605]

>>10983056
Staircases don't have an infinite number of infinitely small steps in a finite distance. Any staircase that did would be a ramp.

[Anonymous No.10994608]

>>10982184
1/3 is 1/3. Once and forever, periodic nums are bullshit use fractional otherwise we'll get noticable unwanted effects on varius calculations.

[Anonymous No.10994614]

>>10986335
Writing infinity as a number is shorthand for taking a limit, just like 0.999...

Really not sure why anyone who doesn't at least understand the concept of a limit is on this board. You know this is a math and science board right?

[Anonymous No.10994625]

>>10988714
It's basically true in real life. Macroscopic objects aren't made of infinitesimal parts. There are no perfect circles, just arbitrarily approximate ones up to a point.

[Anonymous No.10994651]

heres some hot new math i just came up with

[math]\frac{1}{3} = 0.\overline{333}:A[/math]

what does ":A" mean? It's a hexidecimal numeric identifier, used to determine how the number should be read.
>:A= this number is repeating without significant deviation. Direction: Hold 1 more digit than is displayed, and round. [math]0.333:A \rightarrow 0.333[3][/math] 0.333[3] = 0.333; 0.333[3]*2 = 0.666[6] = 0.667; 0.333[3]*3 = 0.999[9] = 1.0
>:B = this number is seemingly repeating but contains significant deviation [eqn]\sum_{n=1}^{\infty} \frac{1}{2^n} = 0.\overline{999}:B [/eqn].
>:C =
>:D =
>:E =
>:F =

>>[math]0.\overline{999}:A \neq 0.\overline{999}:B[/math]
FEEL free to fill these in.

[Anonymous No.10994699]

>>10994604
The entire concept of limits is that some infinities are limited. Like a curve on a plane, which, regardless of length, is made of infinite points. If you can't understand this, you will never be able to do any math or science.

[Anonymous No.10994729]

>>10994699
nothing is made of infinite anything and you're a daydreaming mong living in fantasy land.

[Anonymous No.10994735]

I fucking hate decimals

[Anonymous No.10994751]

>>10994729
Maybe the true math was the infinite friends we made along the integral.

[Anonymous No.10994941]

>>10994729
Math can only approximate physical reality and vice versa, you absolutely retard. The point is that you can approximate at any arbitrary scale. This is shit someone with an IQ of 90 should be able to understand.

[Anonymous No.10995499]

[math]
\displaystyle \sum_{n=1}^{\infty}\frac{9}{10^n} = \frac{9}{10} + \frac{9}{100} +\frac{9}{1000} + ...
= b = \frac{1}{10}(9 + \frac{9}{10} + \frac{9}{100} +...)
= \frac{1}{10}(9+b) = b \\
\frac{1}{10}(9+b) = b \\
\frac{9}{10} = \frac{9}{10}b \\
1 = b
[/math]

[Anonymous No.10995528]

>>10994941
it only takes 62 digits to accommodate the scale of the UNIVERSE in meters with planck length accuracy. How's that for arbitrary you dumb nigger.

[Anonymous No.10995655]

>>10995528
>62 digits
peanuts compared to the amount of ways you can arrange 6.022x10^23 molecules

[Anonymous No.10995774]

>>10995655
meme number.

[Anonymous No.10995858]

>>10995774
less than 20g of water

[Anonymous No.10997184]

bump

[Anonymous No.10997380]

>>10995499
>b = 1/10b
quackematics

[Anonymous No.10997680]

>>10997380
>i have no argument

[Anonymous No.10997701]

>>10997680
>9/10 + 9/100 + 9/1000... = b
>b = 1/10(9 + 9/10 + 9/1000...)
>b = 1/10(b)
>b = 0

[Anonymous No.10997703]

>>10997184
No

[Anonymous No.10998493]

>>10988714

[Anonymous No.10999140]

>>10992876
>>10992880
based basebro

[Anonymous No.10999142]

>>10986459
.333 repeating is exactly 1/3 you dumb nigger

[Anonymous No.10999160]

>>10986727
>Where is the rule that says we can multiply an infinite sum?
If you want to multiply an infinite sum by a single number, it's easy, you just multiply every summand by that number. It's called the distributive law.

[Anonymous No.10999193]

1=1
Q.E.D.

[Anonymous No.10999388]

>>10997701
>>b = 1/10(b)
hurr durr
it's b = 1/10(9+b)
lrn2read

[Anonymous No.10999904]

>>10999142
No, it is not. It is conceptual approximation.

[Anonymous No.10999915]

>>10982184
.333...=1/3 is an approximation retard!

[Anonymous No.10999918]

>>10982393
Wrong. .999... is not a real. It is a hyperreal. And it is sure as hell not equal to 1.

[Anonymous No.10999920]

>>10982769
So let me guess, a parabola touches its asymptotes?

[Anonymous No.11000310]

The absolute state of /sci/

[Anonymous No.11001098]

WELCOME
TO
THE MACHINE

[Anonymous No.11001107]

>>10999904
>>10999915
>>10999918

[Anonymous No.11001932]

>>10982184
Thanks for this shit post. Kinda new to this board, this post made it very clear that everyone here is retarded. This place is an incredibly inefficient way to learn or discuss anything

[Anonymous No.11001950]

>>10999915
>>10994608
This is the answer.
1 div by 3 =! .333
1 div 3 = 1/3, a ratio.
1/3*3=1.
Nothing breaks
Limits and aproctchomations are not needed

[Anonymous No.11003165]

>>11001932
>This place is an incredibly inefficient way to learn or discuss anything
That's here. That's home. That's us.

[Anonymous No.11004962]

bump

[Anonymous No.11006945]

bump lmao

[Anonymous No.11007941]

>>11001932
True for the most part, there are a couple smart people that post here though.

[Anonymous No.11009451]

resurrected from page 10

[Anonymous No.11009488]

Bridging fractions and decimals was never meant to happen. Dont do this. They arent compatible

[Anonymous No.11009497]

>>11001932
Depends what you're trying to learn. Two days ago I learned how to defend my property using a neural net and through botany.