/sci/ - Science & Math

>>9733327
dumb frogposter

How much less than 1 is it?

>>9733344 (checked)
0.000...01

And how many zeros are represented by those ellipses?

>>9733350
As many as I need to reach an infinitely small number.
:^)

A:
0.9 + 0.1 = 1.0
0.99 + 0.11 = 1.10
0.999 + 0.111 = 1.110
0.9999 + 0.1111 = 1.1110
[math]0.\overline{9} + 0.\overline{1} = 1.\overline{1}0[/math]

B:
1 + 0.1 = 1.1
1 + 0.11 = 1.11
1 + 0.111 = 1.111
1 + 0.1111 = 1.1111
[math]1 + 0.\overline{1} = 1.\overline 1[/math]

A = 1.11111...110
B = 1.11111...111

B > A

0.8 + 0.1 = 0.9
0.88 + 0.11 = 0.99
0.888 + 0.111 = 0.999

For a < 0.89, b = 0.111...
a + b < 1

0.88 + 0.111... = 0.99111...
0.888... < 0.89
0.888... + 0.111... < 1
0.999... < 1

>>9733417
>let's pretend infinite is finite

>>9733427
0.8 + 0.1 = 0.9
0.88 + 0.11 = 0.99
0.888 + 0.111 = 0.999


0.88 + 0.111... = 0.99111...
0.888... < 0.89
0.888... + 0.111... = 1
0.999... = 1

What number could be between 0.999... and 1?

For
a < 0.222...3
b = 0.777...
a+b < 1

0.22 + 0.777... = 0.99777....
0.222 + 0.777... = 0.999777...
0.2222 + 0.777... = 0.9999777...

0.23 + 0.777... = 1.00777...
0.223 + 0.777... = 1.000777...
0.2223 + 0.777... = 1.0000777...

0.222... < 0.222...3
0.222... + 0.777... < 1
0.999... < 1

>>9733449
> 8 + 1 = 10

>>9733455
0.9999...

>>9733327
Obviously. Any number not 1 is either smaller or larger than 1, only indoctrinated mathtards would claim otherwise

>>9733462
8+1=9

you're bad at math, this one takes the cake

>>9733455
The number with countably infinite 9's.

>>9733467
>0.888... + 0.111... = 1
>8 + 1 = 9
Choose one.

>>9733348
False unless you're using non-standard notation. Three dots in the middle of a string of numbers suggests a finite amount of numbers, dots at the end suggest infinite.

>Things can be infinite
t. mathtard

>>9733460

0.22 + 0.777... = 0.99777....
0.222 + 0.777... = 0.999777...
0.2222 + 0.777... = 0.9999777...

0.23 + 0.777... = 1.00777...
0.223 + 0.777... = 1.000777...
0.2223 + 0.777... = 1.0000777...

0.222... = 0.222...3
0.222... + 0.777... = 1
0.999... = 1

>>9733472
both

>>9733487
>there is a 3 in 0.222...

>>9733491
3/inf = 0

>>9733492
>there is a 3 in 0.222...

>>9733494
>>9733492

>>9733497
>there is a 3 in 0.222...

>>9733348
As soon as you put a 1 at the end you say you are assuming a finite number, so 0.000...01+0.999...=1.000...0999... where the 1 in 0.00...01 and the last 0 in 1.00...0999... are in the same n position, and you can make n tend to infinite but there will always be other 9s

>>9733515
second this

>>9733479
a circle is and pi is an almost infinite number

>>9733515
0.9 + 0.1
0.99 + 0 01
0.999 + 0.001
0.9999 + 0.0001
0.99999 + 0.00001
0.999...99 + 0.000...01
0.a9 + 0.b1
inject equal n amount of 9's at "a" as n amount of 0's at "b"
0.a9]9 + 0.b0]1
0.a99]9 + 0.b00]1
0.a999]9 + 0.b000]1

[math]0.\bar{9}9 + 0.\bar{0}1 = 1 \\ 0.\bar{9} + 0.\bar{0} < 1 [/math]

>>9733441
I don't get this meme.

>>9733574
orig is "if you sit on your hand 15min it feel like someone else if jacking you off". thats it.

>>9733536
0.[3 + 0.[7 = 1
0.2[3 + 0.7[7 = 1
0.22[3 + 0.77[7 = 1
0.222[3 + 0.777[7 = 1
0.2222[3 + 0.7777[7 = 1

0.222...[3 + 0 777...[7 = 1
>after infinity
0.222... + 0.777... = 0.999...

>>9733475
> m-m-muhh notation

everyone understands the answer, keep your dumb notations up your little bumhole

bumhole >_<

>>9733348
But, 0,(0)1 = 0.

>>9733586
>lying on the internet

>>9733536
So you're saying you write and infinite numbers of 0's and THEN you write a 1?

>>9733592
You write the 1 first, then write an infinite amount of zeros in front of it.

>>9733594
Do do that, please. I'll wait.

>>9733610
Not an argument.

>>9733616
>resorts to shitposting
Good to know you're trolling. For a moment there I thought you were actually retarded.

>>9733633
Meant for >>9733610

[math]\lim_{x\to\infty}\frac{1}{x}=0[/math].

>>9733647
You don't reach infinity though.

>>9733647
x has to be a real number. There is no real number x in 1÷x = 0

What's 0.0...1 + 0.0...9 ?

>>9733649
Why do you need to reach infinity? For all a > 0, there exists b > 0 such that if x > b, then |1/x| < a

>>9733663
0

>>9733676
Makes sense desu. So you just throw away the 1 which had to be carried

>>9733680
0.0...1 = 0.0...9 = 0

>>9733684
How can they be equal when they have different digits in the infinitieth place

>>9733594
How is it possible to say 0.00...(infiniteamountof 0)...001

>>9733692
Infinite 0s means an unending amount of 0s

>>9733703
It's not unending because it ends at infinity

>>9733709
Infinity is unbounded. It never ends

>>9733709
What do you think "ends at infinity" means? You will never be "at infinity" so if it "ends at infinity" then it doesn't end

>>9733720
>>9733711
You can define "ends at infinity" to mean that it ends at the first infinite ordinal.

>>9733722
call it whatever you want, it's still unbounded

>>9733722
But you were taught the ellipses notation in school, and you know that the expansion does not mean to include limit ordinals, right? So what is the relevance?

>>9733722
0.0...1 and 0.0...9 are not equivalent to a cauchy sequence, so they are not real numbers. Define them as an equivalent cauchy sequence that is not equal to 0, go on

>>9733692
1/inf=0

>>9733750
It doesn't have to be a real number. You can define a number like 0.0...1 to mean a function from, say, [math] \textomega + \textomega [/math] to the ordinal 10.

>>9733749
You can extend the definition to include the use of ordinals though. No need to limit yourself to what was taught in middle school

>>9733764
No, you cannot meaningfully extend the definition of a decimal expansion in this way.

[math]
\\ 0 < p < 1
\\
1 = p + (1-p) ~~~~~~\overset{1}{[\overbrace{=====p=====|==(1-p)==}]} \\
= p[x+(1-x)] + (1-p) ~~~~~~\overset{1}{\overbrace{\underset{p}{[\underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\
\\
\dfrac{x}{p-x}=\dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow x=p^2 \Rightarrow (p-x)=p(1-p)\\
\overset{1}{\overbrace{\underset{p}{[\underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\
\\
\dfrac{p^{n+1}}{p^n(1-p)}= \dfrac{p}{1-p} \Rightarrow \dfrac{p}{p}=1\\
\overset{1}{\overbrace{\underset{p^2}{[\underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\

[/math]

Let us suppose, contrary to our hypothesis, that [math] 1=0.\overline{9} [/math]. It follows whencely that [math] 1-0.\overline{9}=0 [/math] and [math] 1-\frac{1}{0.\overline{9}}=0 [/math].
But, alas, [math] \frac{1}{0.\overline{9}}=\frac{1}{\sum\limits_{n\geq 1}9\cdot 10^{-n}}=\sum\limits_{n\geq 1}\frac{1}{9}\cdot 10^n \longrightarrow\infty \neq 1 [/math]; A contradiction! Hencely, [math] 0.\overline{9}\neq 1 [/math].
Clearly, [math] 1\not<0.\overline{9} [/math]; and whenceforth [math] 0.\overline{9}<1\quad \text{Q.E.D.} [/math].

>>9733806
KEK

This is why logic is inherently flawed. You can use as many little theorums and whatnot as you want, but its less than one, It just is. Look at those two numbers. One is less than the other. A small amount is still an amount.

Scientism is cancer.

>>9733646
>no u

>>9733845
how much less than one is it?

>>9733854
It doesn't matter. Look at the two numbers.

>>9733536
0.9...9 + 0.0...1 = 1
0.9... + 0.0... = 1

>>9733878
>lookie-lookie math
what's next, more kindergarten doodles?

>>9733888
Go ahead and keep uselessly argueing inanities that are only allowed by following inherently flawed logic, irrespectable to reality.

Idiots living in bubbles.

>>9733894
>insult math
anything but a rigorous proof or even a descent citation.
just another day at the /sci/ crackpot day care center

>>9733894
>insult math
Anything but a rigorous proof or even a decent citation.
Just another day at the /sci/ crackpot day care center.

>>9733905
The proof is there and you just ignore it, pretending like it doesn't matter.

>>9733327
>Declaration: In this post everything is assumed to happen in the space of real numbers unless explicitly stated otherwise (WHY?)
>Lemma 1.01: for all x < 1; we can find C > 0 s.t. (x + C) < 1
Proof: Think
>Corollary 1.02: for all C > 0; 0.999... + C > 1
Proof: follows directly from Lemma 1.01
>Theorem 1.03: 0.999... = 1
Proof: left as an exercise for the reader. [math]\square[/math]

>>9733909
Publish it, disproving all modern math & win your Fields Medal.
Don't waste it on us.

>>9733918
You're still missing the point completely.

>>9733927
>>9733905

>>9733845
>This is why logic is inherently flawed
Then why should anyone listen to anything you have to say? By what means have you to convince them after telling them to abandon logic? Is it that you hate deduction, don't understand it, or are simply trolling?

>>9733654
it's a limit dumbass

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

>>9733927
You are the one missing the point.

>>9733952
Delete this

>>9733327

three > 3

>>9733952
[math]
1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}
[/math]

we are fucking at it again

>>9733967
What a useless proof, people that think 0.999... < 1 also think that 0.333... < 1/3

>>9733970
Can you say 'again' if it never actually stopped after it began?

>>9733980
no, the calculator experience is quite different

>>9733980
1/3 = 3/10 + 1/30 = 0.3 + 1/30
= 0.3 + 3/100 + 1/300 = 0.33 + 1/300
= 0.33 + 3/1000 + 1/3000 = 0.333 + 1/3000
= 0.333 + 3/10000 + 1/30000 = 0.3333 + 1/30000
= 0.333... + 1/inf = 0.333... + 0 = 0.333...

>>9734005
it stopped for a at least month but resumed now maybe the master-baiter was busy

>>9734022
"it rubs the lotion on its skin or else it gets the rash again"

>>9733967
You can't prove that [math]\frac{1}{3}[/math] is functionally equal to [math]0.\bar{3}[/math]. You've confused two different numbers systems to be indicative of the same thing. Fraction numbers have infinite arbitrary accuracy. Decimal numbers are bound by the tens.
[math]\frac{1}{3}[/math] isn't the same value as [math]0.\bar{3}[/math]

>>9734147
lol

>>9734019
So your logical fallacy belief that 1/3 = 0.333... relies on the fact you believe infinity is a real number that can be incremented to?

Really makes ya think.

Feel free to entertain what a value [math]\frac{n}{\infty}[/math] might be, but you're more than just a little 'tarded if you think you can increment to an infinite'th step in infinite work.

>>9734147
>Fraction numbers have infinite arbitrary accuracy. Decimal numbers are bound by the tens.
[citation needed]

>>9734169
>infinity is a real number
nope, the definition precisely says that it isn't a real number

https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

>>9734169
No, it doesn't rely on infinity being a real number that can be incremented to. 0.333... = 1/3 can be shown using the definition of repeating decimals

1/9 = .11111...
8/9 = .8888...
9/9 = .9999...

9/9 = 1

This is how it was explained to me and I don't see how you can argue against it...

>>9734183
You don't understand, fractions and decimals are 2 different number systems, you are confusing the 2 to be indicative of the same thing

>>9734186
>You don't understand
lol

>>9734187
Thanks

>>9734186
What does this even mean, actually?

Because it sounds like you're saying decimals and fractions and two different types of math that can't connect to each other.

Which sounds so retarded that I simply must be misunderstanding something.

>>9734147
To be cear, by infinite i mean unlimited here. There is no false fraction, the truthfulness only comes from trying to evaluate it to a different number system.

A number [math]\frac{1}{3}[/math] is perfectly fine just being "one third". It doesn't need to be evaluated to a decimal to even perform arithmetic. We can all do [math]\frac{1}{3} × 3 = \frac{3}{3} = 1.0[/math], and this is a truthful evaluation since [math]\frac{n}{n} = 1[/math]. What is a false evaluation is [math]\frac{3}{3} = 0.\bar{9}[/math], because therre exists no mode or method dividing a sole 3 into another sole 3 which returns any amount of 9's.

>>9734186
1/4 isn't 0.25

u see dey has mystical difference

>>9734176
Hmm... did you uh... read the post you replied to? Or are you a bot?

>>9734190
your welcome, the citation earned it

>>9734196
ty for your contribution

>>9734193
word salad bullshit

citation needed

>>9734204
You are confused. I didn't ask a question or post my opinion. I posted a statement

>>9733327
[math] \displaystyle 0.999\dots = \sum_{n = 1}^\infty 9\bigg(\frac{1}{10}\bigg)^n = \frac{\big(\frac{9}{10}\big)}{1 - \frac{1}{10}} [/math]

Sage. Stop arguing about this nonsense, take calc 2.

>>9734211
citation needed

>>9734212
Oh no, sage, the downvote of 4chan :O

>>9734219
>i have no argument

>>9733806
>reciprocal of a sum is the sum of the reciprocals
(You)

>>9734221
You're the retard that fell for this stale bait

>>9734204
>it's you again
Did your ban expire? Weren't you humiliated enough in your last thread? Or did you want more punishment?

>>9734212
>[math] \displaystyle 0.999\dots = \sum_{n = 1}^\infty 9\bigg(\frac{1}{10}\bigg)^n = \frac{\big(\frac{9}{10}\big)}{1 - \frac{1}{10}} [/math]
cool. where did you learn about this one?

>>9734233
infinite geometric series

>>9734231
Can you link me to who you think I am from the last thread?

>>9734238
neat ive never seen it before,. thanks!

>>9734240
I got lazy and quoted you when I wasn't sure. I'm referring to the OP of the last thread since you were kind of talking like him. He's in here somewhere for sure.

>>9734246
Why would the OP from last thread argue against 0.999... < 1 if he started the thread?

>>9734224
fucking kek you are hilarious
run n up to 10 and see how bad you are at math

>>9734233
Here's an explicit limit for the curious
[eqn] 0.\bar{9} \equiv \sum_{n=1}^{\infty} \frac{9}{10^n} = \lim_{k \rightarrow \infty} \frac{9}{10}\frac{1-\frac{1}{10^k}}{1-\frac{1}{10}} = \frac{\frac{9}{10}}{1-\frac{1}{10}} = 1 [/eqn]
Note that the triple equals sign indicates a definition, this is actually how a repeating decimal is defined.

inf - (inf - 1) =/= 0
inf - (inf - 1) = 1
1 - 0.999... = 1/inf
1/inf =/= 0

>>9734249
because logic is for pussies

>>9734250
Lol you're such a retard, you don't even know

>>9734255
sound like fapping under a blanket

>>9734250
In case you thought i was agreeing with the green text statement, I was mocking it.

>>9734257
actually he's right. i posted the proof so im pretty sure its correct.

>>9734263
Lol no, your proof is wrong

>>9734266
i think i would know if my proof was wrong faggot

>>9734263
see
>>9734261

>>9734268
No you wouldn't because you're a retard

>>9734261
>you thought i was agreeing with the green text
t'was so, good then, good
*puts wet trout down*

>>9734268
a/(b+c) != (a/b)+(a/c)

>>9734195
You are dumb and didn't learn how to perform division and don't understand the concept of a remainder.


1 ÷ 4 = ???
1 - 4
1(0) - 4×[2] = 2 <----
2 - 4
2(0) - 4×[5] = 0 <----

1÷4 = 0.25

0 - 4
0(0) - 4
0(00) - 4
0(000) - 4

[math]\frac{1}{4} = 0.25\bar{0}[/math]
This value has terminating zeros. It is a unique result indicative of final precision.

1 ÷ 3 = ???
1 - 3
1(0) - 3×[3] = 1
1 - 3
1(0) - 3×[3] = 1
1 - 3
1(0) - 3×[3] = 1
...
1 ÷ 3 ≈ 0.333...
...
[math]\frac{1}{3} \approx 0.\bar{3}[/math]
The value lacks terminating zeros. It is not in final precision.

Now for something really funny, cause higher math is gay and retarded.
Lets switch this up a little and go back to pretending an infinite'th step in infinite work is achievable (it really isn't, but we'll pretend for the mathlets)
[math]\sum{n=1}^{\infty} \frac{3}{10^n}[/math]
You imply that at n=infinity, [math]\frac{3}{10^{\infty}}[/math] is equal to 0.
Well guess what, you just got your final precision didn't you. You know what else you got? A unique number. You multiply [math]0.\bar{3} × 3 = 0.\bar{9}[/math] and what you have is an infinite string of 9's with a final 0 at the end, which makes it a seperate and unique number that clearly isn't 1. Even if we simply rounded on the last possible digit, it's just a zero so it rounds down unchanging instead of rounding up to 1.

Since infinite sums are not how most people craft numbers or assume to perform division, we can just assume an infinite sum identity of 3/10^n is not really the same as 1/3. But dang, is it close!

>>9734276
how about when a=b=c=1 then?

>>9734278
There you are, I was wondering when you'd show up. You fucked the latex up again, give up.

>>9734278
and the mustaches and sombreros? where did they go?

>>9734279
It's not true for all real a,b,c, only in some cases. a=b=c=1 is not one of those cases

>>9734260
>numbers emit sound

>>9734280
shitlatexman is a legend
a kind of crazy 4chan pet
give him a crumb every now and then
and he'll bark happily all day

>>9734291
I know
>that time he argued that [math] 0.\bar{3} \neq \frac{1}{3} [/math] because floating point numbers aren't precise enough.

>>9734278
>infinite string of 9's with a final 0 at the end
my sides

>>9734270
i have seen it
>>9734274
please do not call me the word RETARD. thank you

>>9734297
What's the problem, brainlet?

>>9734299
ok, Mr Retardo

0.3 + 0.7 = 1
0.2 3 + 0.7 7 = 1
0.22 3 + 0.77 7 = 1
0.222 3 + 0.777 7 = 1
0.2222 3 + 0.7777 7 = 1
0.22222 3 + 0.77777 7 = 1
0.222222 3 + 0.777777 7 = 1
...
[math]0.\bar{2}3 + 0.\bar{7}7 = 1[/math]
>b-but n-nothing comes after infinity...
[math]0.\bar{2} + 0.\bar{7} \stackrel{\neq}{<} 1[/math]

>>9734301
my sides, can't you read?

>>9734306
Ok, brainlet

>>9734294
The decimal system isn't precise enough you concave skulled mongoloid. Lmao
Wtf does it have to do with floating point. Computers print results in the decimal system just like you do.

>>9734304
0.2...3 + 0.7...7
= 0.2... + 0.7... = 0.9... = 1

good boy! you got one right!

>>9734313
AHAHAHAHAHAHAHAHAHAHAHA

>>9734315
You're off by 0.000...1

>>9734315
Oh dang looks like you got that wrong cause you don't read too good.

Must have missed the obvious unequal and lesser than signs.

I'm sure if you read the post at least 7 more times, you'll find them.

>>9734320
0.0...1 = 0.0... = 0

another one!
patpatpat

>>9734322
>unequal and lesser than signs
sorry, won't touch your shitlatex
haven't got any dogpoo baggies with me

>>9734327
Latex confuses you?
Damn buddy. You might be on the wrong board.

>>9734335
AHAHAHAHAHAHAHHAHAHAHHAHAHAHAHAHHAHAHAHHHAHAHAHAHAHAHHAHAHAHAHHA
please keep going, this is fucking hilarious

>>9734335
Math confuses you?
Damn buddy. You might be on the wrong board.

>>9734344
You're the one who thinks 2 + 7 = 10

>>9734324
Still off by 0.000...1

>>9734345
in base nine it does

>>9734345
oh my god, you can't be this dumb, i refuse to believe it
AHAHAHAHAHAHAHAHAHAHAHA

>>9734345
>0.222... = 0.2

>>9734349
Ye, well computers don't print in base 9 and neither does the world. We use the decimal system.
Decimal, you know
DEC
base 10

>>9734356
>computers
>relevant to this conversations
*breathes in*

>>9734356
You're a real nigger, aren't you?

>>9734356
your iq, can see why you're attached to it

>>9734354
Be a good little girl and learn to do math

Left to right, add each element vertically
0 . 2 2 2 2 2 2 2 2 ...
0 . 7 7 7 7 7 7 7 7 ...
___________________

I'll start you off sweetie, no curveballs.

0 . [2] 2 2 2 2 2 2 2 ...
0 . [7] 7 7 7 7 7 7 7 ...
____________________
0 . 9 - - - - - - - -

Can you fill in the blanks, honey?

>>9734368
0.999...

>>9734368
1.00000000000000000000000000000000

>>9734224
Why am I surprised that a brainlet like you would be lost in the delicacies and intricate subtleties of my clever proof. Here's a proof that even a little brainlet like you might comprehend one day (it took me 5 minutes):

Allow us to define [math] \operatorname{f}(n)=\underbrace{0.999\cdots 9}_{n\text{ times}} [/math]. Using induction on [math] n [/math], proceed.
Basis of induction: most certainly [math] \operatorname{f}(0)=0<1 [/math].
Induction hypothesis: suppose thus: [math] \operatorname{f}(n)<1 [/math] for all [math] k\leq n [/math].
Induction step: henceforthwith [math] \operatorname{f}(n+1)=\operatorname{f}(n)+\underbrace{0.000\cdots 0}_{n\text{ times}}9 [/math]. Hark! [math] \operatorname{f}(n+1)<1+\underbrace{0.000\cdots 0}_{n\text{ times}}9 [/math].
However; [math] \underbrace{0.000\cdots 0}_{n\text{ times}}9\longrightarrow 0 [/math] and thence [math] \operatorname{f}(n+1)<1 [/math] as required. [math] \mathbf{Q.E.D.} [/math]

[math]0 \rightarrow \infty = \overbrace{\underbrace{0,1,2,3,4,\cdots}_{\infty \text{ elements of } \mathbb{R}}, \underbrace{\infty}_{\text{not in } \mathbb{R}}}^{\text{all possible elements}} \\ \text{Mapped between 0.9 and 1} \\ 0.9 \rightarrow 1 = \overbrace{\underbrace{0.9, 0.99, 0.999, 0.9999, \cdots}_{\infty \space \mathbb{R} \text{ elements of the map}}, \underbrace{1}_{\text{not in the }\mathbb{R}\text{ map}} }^{\text{all possible elements}} [/math]
If there exists a value to bridge the gap between 0.999... and 1 thus allowing 0.999... = 1, there also exists a value to bridge the gap between real numbers and infinity, thus allowing infinity to be equal to a real number.
If there exists no value to bridge the gap between 0.999... and 1 thus assuming 0.999... = 1, there also exists no value to bridge the gap between real numbers and infinity, thus assuming infinity to be equal to a real number.

Because the value does not actually exist and infinity cannot be reached, there is no possible value to add to 0.999... to make it reach 1; it will never reach 1. No amount of increments in the reals will reach infinity, so no mapped amount of increments between 0 and 1 will reach 1.

0.999... is not "infinitely close" to 1. It is actually infinitely far away from 1. Any arithmetic that shows 0.999... = 1 is therefore flawed by making inconsistent and mistaken assumptions about the construction of a repeating decimal extended from a poor interpretation and implementation of infinity, because infinity has classically always been poorly interpreted and implemented.

[math]0.\bar{9} \neq 1 [/math]

If there is not value in between 0.999... and 1, does that really mean that they are equal?
There is no integer between 3 and 4, but 3 doesn't equal 4.

I understand the 'proof'
x = 0.999...
10x = 9.999...
9x = 9.999... - 0.999... = 9
x = 1

Would this be more intuitive in another base?

>>9734374
>let's pretend infinite is finite

>>9734381
and where did i do that

>>9734379
>1 not in R
kek

>>9734374
Congrats, you have proven that 0.999...9 < 1 for any n amount of 9s where n is a natural number

>>9734383
"n", "n times", "n+1"

>>9734374
This is a correct proof, but not of 0.999... < 1. Your original proof >>9733806 is still wrong

[math]
\\\frac{3}{3} = 1\\\\
\frac{1}{3} = 0.333...
\\\\\frac{2}{3}=0.666...
\\\\\frac{3}{3}=0.999...

>>9734374
>delicacies and intricate subtleties of my clever proof
lol, delusional retard see >>9733815

>>9734393
Tfw to smart too latex properly

>>9734385
Since attaining infinity is impossible, any attempt at doing so only gives you a real number. Not him btw but you should be smart enough to know you can't increment to a value equivalent to infinity. Whenever you decide to give up, there's your real number.

>>9734393
>>9734399
Here is my proof ur all faggots and these threads should be banned

>>9734407
that is not a proof. it is four statements presented as equalities

>>9734407
>[math]\frac{3}{3} = 0.999[/math]
Hm.. which calculator did you use to determine this? Mine just says it's 1.

>>9734411
Dont caare mathtard

>>9734415
Microsoft Word

>>9734415
Calculators are too brainlety to realise 0.999... = 3/3

>>9734415
1/3 = 0.3...
+
2/3 = 0.6...
=
3/3 = 0.9...

>>9734374
This is an absolute garbage induction proof. You haven't shown that f(n+1) < 1.
0.000...09 goes to 0 as n goes to infinity doesn't prove your induction step

>>9734404
Which is why induction doesn't work here, retard

>>9733327

>>9734374
Agreed, 0.999...9 with n number of 9s is less than 1.

>>9734421
1/3 = 0.3 ?

Since when?

>>9733344
It's 1 - 0.999... less than 1.

>>9734372

>>9734435
https://en.wikipedia.org/wiki/Ellipsis#In_mathematical_notation

>>9734446
Oh so you meant 1/3 = 0.33 ?

>>9734452
https://en.wikipedia.org/wiki/Repeating_decimal

>>9734452
>>9734176

>>9734393
>>9734399
I'm beginning to think your computer doesn't render latex if you see a lot of \\

>>9734453
Ah. Ok.

1/3 = 0.333

I'm pretty sure thats still wrong though. 1/3 is larger than that.

>>9734458
You are wrong, 1/3 is exactly 0.333

>>9734393
>[math] \\\frac{3}{3} = 1\\\\
\frac{1}{3} = 0.333...
\\\\\frac{2}{3}=0.666...
\\\\\frac{3}{3}=0.999... [/math]
im beginning to think it wont render if you dont close your tags

>>9734461
Nah, it renders fine for me

>>9734458
right. inf=3
patpatpat

>>9734459
But that means 0.333 × 3 = 0.999

And if 1/3 exactly equals 0.333, and 1/3 × 3 = 1, then 0.9991 > 1

Hmmm...
Something smells fishy.

>>9734463
Infinity is a number amount, right?

>>9734466
Our intuition isn't already right

>>9734470
>>9734454

>>9734466
>>9734477

>>9733350
The same number as those many nines are represented by those ellipses.

>>9734463
[math] \frac{1}{3} = \frac{11}{33} = \frac{111}{333} = \frac{1111}{3333} = \frac{11111}{33333}[/math]
The number amount of 1's over 3's here doesn't matter. You can remove 4 factors of work from [math]\frac{11111}{33333}[/math] to get [math]\frac{1}{3}[/math] and the problem has not changed.

You can remove all but one of the infinite factors of work from 0.222... + 0.777... = 0.999... to get 0.2 + 0.7 = 0.9

the same work was performed on each piece of the equation.
Infinite 2's were removed from 0.222...
Infinite 7's were removed from 0.777...
Infinite 9's were removed from 0.999...
The problem has not changed because each part of the equation was equally transformed.
0.2 + 0.7 = 0.9
0.2 + 0.7 < 1

0.222... + 0.777... = 0.999....
0.222... + 0.777... < 1

Now remember, the problem has not changed.

0.999... < 1

Some problems never change.
1/3 > 0.3
1/3 > 0.33
1/3 > 0.333
1/3 > 0.3333
1/3 > 0.33333
1/3 > 0.333333
1/3 > 0.3333333
1/3 > 0.333...
It doesn't matter how many extra 3's there are. If you can only ever append more 3's, there will always be a remainder, and if theres a remainder it's always unequal in flat decimal, and if it's always unequal then this evaluation only produces a result that is less than the fraction.

>>9734477
Well if infinity isn't a number amount then what're we crying about. It means 0.999... doesn't have infinite 9's.

>tfw you graduate as a math major

>>9734502
0.33 < 1/3 < 0.34
0.333 < 1/3 < 0.334
0.3333 < 1/3 < 0.3334
0.33333 < 1/3 < 0.33334
[math]0.\bar{3} < \frac{1}{3} < 0.\bar{3}4[/math]

>infinity exists

>>9734506
inf isn't inf
*retards clapping*

>>9734502
you took a strange leap from a partial sum to a limit of an infinite series there.

1/3 in a base system that's divisible by 3 doesn't have to be represented with repeating digits. We should someday teach all of society to use a base with more small prime divisors. We shouldn't worry about the larger one's since these idiots won't ever find them anyways.

>>9734233
University?

>>9734502
>you can only ever append more 3's
infinity isn't a real number
get your head out of your ass already

>>9734252
Glad to know theres still people that actually have studied higher maths here in /sci/

>>9734233
https://youtu.be/XFDM1ip5HdU?t=5m20s

Infinity doesn't exist.

>>9734659
since you're just an asshole, which is nothing but a hole - you don't exist

>>9734670
Yet I can post here.
Can infinity do that ?

>>9734676
0.999...=1
1 shitposter detected

it just might

>>9734530
>existence exists
Hah

>>9734659
If the math world yes, in the real world no.

>>9734459
False

>>9734404
>I don't understand what numbers can be real numbers

>>9734659
Last time I Iectured elliptic curves, infinity certainly existed for each curve. You have new information?

>>9733967
the mental gymnastics played here

>>9734886
awww, it's retarded

>>9734374
You literally assumed infinity is a natural number here
idiot

>>9734646
that's not higher math but thanks anyway anon

>>9734720
Infinity doesn't exist in any world. Making up a googoogaga fantasy term doesn't mean it exists in any way but the most granted that saying a word means the word exists. Infinity as a number isn't really a thing, much likes elves and orcs and the one ring are not really things. Keep your LOTR fictional fantasy math to yourself and out of the education system.

>>9734949
why are preteens allowed here, send this brat back to mommy

why do we waste our time shitposting about this time and time again?

>>9734384
If you map each integer 0 to infinity to be real numbers between 0 and 1, there is no amount of incrementing in the map between 0 and 1 which will reach 1, so 1 is not in the real map. If you're not a total brainlet, you should already be able to tell that this is the equivalent of mathlet's calculus "converging to 1", aka diverging to infinity.

>>9734957
Wrong
Proof: [math] \text{Think} [/math]

>>9734959
Wrong
Proof: think

Anyone can eyeball what 9/10th's of an apple looks like. Even though an apple isn't a number, it still has volume and size which means it can be measured and divided.

What is 9/10ths of infinity?
Doesn't exist. Infinity has no knowable size or length or volume.
What is 9/10ths of 1?
Well thats easy, its 0.9

So if you have the sum [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] this value approaches 1 but cannot reach 1, just like [math]\sum_{1}^{\infty} 1[/math] approaches infinity but can't reach infinity.

What your atrophied sac of shit brain fails to understand is that the limit is an analog for infinity. If your limit is 1, all possible values exist under 1, and none exist at or beyond 1. You've confused the analog for the literal real number 1 that naturally preceeds 2 and 3 and 4 and the rest of all real numbers.

But you didn't know that, did you?
Cause you don't think about the things you were taught. You just absorbed them like a janitor's mop soaking up the piss and shit you leave in the public bathroom. You absorbed them and regurgitated them when asked to provide answers on indoctrination tests. Here's your B+, you were a good goy swallowing all that garbage and puking it back up. Good little retard.

So again my dirty little beaner brained boy wonder, what is 9/10ths of infinity?

The answer is: (You)'re a subhuman, subanimal fucking hellbound mongoloid commanding an existence less substantial than a pebble.

>>9734959
Thanks Professor Layton

>>9734973
>this value approaches but cannot reach 1
correct, but it can be made as close as you want to one, for any level of precision, i can give you a partial sum that is precise enough. This means that it never "reaches" one but can get arbitrarily close to 1. We call that number that it cannot reach but can be made arbitrarily close to the "limit". The infinite sum isn't saying we're adding up an infinite number of terms, it just asks "what's the limit?" which is 1. Do you understand why it's called a "limit" now?

>>9734973
The sum symbol doesn't say "add up terms until it reaches one" it says "what's that number that it can't reach but can be as close as we want to?" and that number is 1, as you said. The series is DEFINED to be that number it cannot quite reach, a series is not an infinite sum of terms, it's a convenient way to represent that limit.

>>9734983
You're evaluating wrong by all accounts if if you believe the infinite sum limit of 9/10^n isn't solely just 0.9 repeating.

Again, what is 9/10ths of infinity?

What is 0.99999... of infinity?

What don't you get here fag?

You're confusing the analog of infinity, the limit of 1, with the real number 1. Its not the real number 1. Its an analog of infinity. You are not getting close to 1, you're only getting close to 0.999....

You can't get arbitrarily close to infinity. It doesn't exist, jose.

>>9734973
your [math] \sum_{1}^{\infty} 1[/math] isn't a well defined statement. Where's your index of summation?
>>9734986
Wrong.
Due to the Archimedean property of [math] \mathbb{R} [/math], there is no difference between [math] 0.\bar{9} [/math] and [math] 1 [/math]. To assert that there is a difference you would violate the definition of [math] \mathbb{R} [/math]

>>9734986
Please keep posting, this is comedy gold.
Dance monkey, dance.

>>9734938
I meant higher as in above highschool level.

>>9734986
>Again, what is 9/10ths of infinity?
[math] \infty [/math]
What is 0.99999... of infinity?
[math] \infty [/math] [math] \text{Why?} [/math]
>analog of infinity
nonsense
>infinite sum
no such thing, it's a series, not a sum. It's a limit, not an addition of infinite terms (because that's not possible)
>Its not the real number 1
Wrong
>you're only getting close to 0.999....
Which happens to equal 1.
>You can't get arbitrarily close to infinity.
Reals can be made arbitrarily large, this fact is trivial.

>>9735023
Close how?
How close?

Lets take a sum of partials sums over 9/10^n up to an arbitrary point

0.9999...99 <---- n-1, previous
0.9999...999 <---- n, current
0.9999...9999 <---- n+1, next

So how close to 1 are you? It's certainly not within 1 element. So is it 2 elements?
10?
How close do you actually think you are to 1?

Are you confusing infinite arbitrary accuracy with knowable accuracy?
Like are you confusing that if 10 decimals are required, 0.999999999 is arbitrarily close to 1?
Do you not understand there is no implement of required decimal accuracy, and that the only limit of work is the balue to which n increments to, which is fucking infinity aka never ending?

You dont have to fill 10 decimals
You have to fill infinite decimals

Heres you:
0.9999999999

Heres the fucking requirement:
0.9999999999xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx...

Fill in all the fucking decimal places nigger. Then you can start talking about "being arbitrarily close" to 1.

>>9735023
>"9/10ths of infinity exists"
>"it's infinity"
I can hear your neurons screaming from here.

>>9733344
It's infinitely close to one but does not reach one.

>>9735040
>How close?
arbitrarily
>So how close to 1 are you?
arbitrarily close
>Are you confusing infinite arbitrary accuracy with knowable accuracy?
this question is nonsensical, try again
>You have to fill infinite decimals
Wrong, all I need to do is show that for any degree of accuracy I can provide a finite string of 9s that is at least that accurate.
>>9735053
[eqn] \lim_{n \rightarrow \infty} n = \lim_{n \rightarrow \infty} \frac{9}{10}n [/eqn]

>>9735058
You are desperately, desperately confused.

[math]\sum_{n=1}^{5} \frac{9}{10^n} = 0.99999 [/math]

This is what happens if change your max iteration to a real. Doesn't look so arbitrarily close to 1 now, does it. If you did it to 6 instead of 5, but still only used 5 decimals of accuracy, you're still just getting 0.999999 and you're still just making it 0.99999

you are using some made up fantasy rules for truncation that I know you didn't learn in an educatiom environment, so if you're digging that deep still trying to justify your garbage education then I will elect on your behalf to bow out of this argument.

Honestly dude, you're shameful.

>>9735067
>You are desperately, desperately confused.
False.
>This is what happens if change your max iteration to a real.
That has nothing to do with this argument.
>Doesn't look so arbitrarily close to 1 now, does it.
Of course, that's a finite number. But I can choose a finite sequence that is as close to 1 as i want it to be, and I can do that for any degree of accuracy.
>you are using some made up fantasy rules for truncation
Why are you truncating an infinite decimal? Your CS brainlet operations are irrelevant.
>Honestly dude, you're shameful.
I'm not the one posting nonsense on the internet like a fool.

>>9735057
What exactly does it mean for a number to be infinitely close to something?

This is why I hate math. Logically it should be the .999... should not equal 1.0. It is extremely close but will not reach zero.
However, mathematically .999...= 1 because of how extremely close they are.

>>9734931
i would never assume such a thing

true

Ah fuck, typo.

>>9735076
There are an infinite amount of 0.999... values greater than 0.999... and less than 1. Thats not really close at all. There are a literal infinite amount of values between 0.999... and 1.

>>9735058

>>9733468

>countably infinite
gr8 b8

>>9735076
If you use your usual field axioms and order axioms (for real numbers), it's perfectly logical.

>>9735074
Here's the definition of infinitely close
For [math] f\colon \mathbb{R} \mapsto \mathbb{R} [/math]
[math] \forall{\epsilon > 0} \, \exists{\delta} [/math] such that [math] x >\delta \implies |f(x) - y| < \epsilon [/math]

>>9735094
where [math] f(x) = y [/math]

>>9735094
0.999... does not satisfy that.

>>9735094
Nice to see you passed calculus 1, anon. How's calc 2 going for you?

>>9735098
Can someone good at analysis give a better definition please? I'm too brainlet

>>9735086
Not an argument

>>9735102
>finite 9's = infinite 9's = 1
>implying your skull isn't collapsing at this very moment

>>9735110
Wrong, is english not your first language? Learn to read.

>>9734993
I imagine if you had enough money to attend school, you'd really enjoy it. Every class would make you laugh your ass off.

>>9735115
>he paid to attend school
LOL
exactly how dumb are you? What's it like living with a disability?

>>9735099
I develop a framework transfinite analysis here
>The General Relevance of the Modified Cosmological Model
>http://www.vixra.org/abs/1712.0598
which shows that 0.999<1, but you can find everything about that part of it in what are already called hyperreal numbers
>https://en.wikipedia.org/wiki/Hyperreal_number

>>9735120
Cranks never fail to entertain
>couldn't even get on arxiv

>>9735113
> I can choose a finite sequence that is as close to 1 as i want it to be
>all I need to do is show that for any degree of accuracy I can provide a finite string of 9s
You are actually retarded dude. You wrote this.

You keep arguing 0.999... = 1 and now you've just said twice in two posts that you're only presenting a finite string of 9's.

Dont you have a fucking social worker care taker or something? A parent? They need to pull you off the computer. You are a squirmy, creepy, pathological liar and an absolute stubborn prick when it comes to learning useful and new information. I know underage ban is a thing but what about bans for an underage mental proficiency? Cause you're truthfully only behaving the way an autistic 14 year old would.

>>9735126
Since I can provide a finite string for ANY degree of accuracy, the limit exists. This is not a difficult concept.

>>9735118
Ah, you're european. That explains a lot. Socialized education kek

>>9735126
>Dont you have a fucking social worker care taker or something? A parent? They need to pull you off the computer. You are a squirmy, creepy, pathological liar and an absolute stubborn prick when it comes to learning useful and new information. I know underage ban is a thing but what about bans for an underage mental proficiency? Cause you're truthfully only behaving the way an autistic 14 year old would.
lmao
This would make good copypasta

>>9735129
Ever heard of a scholarship? I'm american, european schools are a joke

>>9733487
>0.222... = 0.222...3
U wot m8

>>9735136
Scholarships aren't free rides unless you spend the pittance on the cheapest of shitty schools. If that is what you're admitting you've done, you're a retard for wasting your scholarship.

Also you have to be smart to get a scholarship so who do you think you're fooling?

>>9735141
Ivy league schools have the most generous scholarships anon, only brainlets pay to go.

>>9735141
>you have to be smart to get a scholarship
lolno

>>9735142
Right. You're an ivy league graduate who rode a generous scholarship cause you're so smart, and now you spend all day fucking up basic calculus on 4chan...

Right...

So where is your social worker...? Do they only check on you twice a day or something?

>>9735146

>>9735149
Your reddit spacing and weird references to social workers gives you away as that crank that keeps saying [math] 0.\bar{9} \neq 1 [/math]. Opinion discarded.

>>9735154
>reddit spacing

>>9735155
Stupid crank

>>9733348
Okay, sure.
But what's between that number and 0?

>>9733348
No such number in [math] \mathbb{R} [/math], due to the Archimedean property.

>>9735121
Your destruction will entertain me.
>couldn't even save his friends and loved ones

>>9735202
[math]^*\mathbb{R}[/math] are the droids you're looking for
>https://en.wikipedia.org/wiki/Hyperreal_number

>>9735225
Crank-kun, I said that there's no such number in [math] \mathbb{R} [/math], of course there's such a number in [math] ^* \mathbb{R} [/math]

Why are we still arguing this? 0.999... < 1

Even though the Earth is close to a perfect sphere it's not a perfect sphere.

>>9735254
Provably wrong.

>>9735126
Go hang out with the flat earthers, you'll feel right at home.
How does this equality make you feel? Stupid crank.
[eqn] \sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6} [/eqn]

>>9733344
>the easiest thing to say that shuts down all retards claiming 0.999... < 1.

Suppose it is strictly less than 1. What's the difference?

>>9735345
They'll say 0.(0)1, they'll never listen.
One of them said it's "because of computers"

nobody with the 1/3 * 3 """demostration""""" yet?

>>9735235
You are going to be 10/10 surprised at what happens when I get my hands on you. I don't like it when you call me crank.

>>9735235
>>9735386
>>9735386
you... or the engineer that wrote your software.

>>9735297
but it's still not 1 because it's smaller, no matter how much repeating numbers it has. It's getting close, but no dice.

>>9734973
9/10 * inf = inf

>>9735417
>treating inf as a real number
get out of the field, there's a game going on there

>>9735434
Then 9/10 of 1 when the limit is 1 is just 1

9/10 = 1

Great job you fucking ape.

>>9735479
9/10s of an unbounded quantity is an unbounded quantity, what's so hard to understand?

>>9735343
WAR

UHN

GOOD GOD

what is [math]\frac{\pi^2}{6}[/math] good for.
Absolutely nothin
SAY IT AGAIN

>>9735495
[eqn]\sum_{n=1}^{1} \frac{9}{10^n} = 1[/eqn]

>>9735479
so you're saying 1 = inf
*retards clapping*
eat some more crayons

>>9735375
>i can only count using crayons and sock puppets

>>9735525
No, limit = infinity

When you have a limit, no value can reach or exceed the limit. Much like when you have access to the range of all numbers, no value can reach or exceed infinity.

The limit is an analog for infinity.

Did you learn something today or are you going to keep putting your faith on the eternally unobtainable.

>>9735566
lim x, as x->1
where was inf again?

>try the pink crayon, it's delicious

>>9734986
>What is 9/10ths of infinity?
[math]9\overline{0}[/math]
>What is 0.999... of infinity?
[math]\overline{9}[/math]

>>9735585
Analog

You can remember the word better next time by thinking of anal and your scheiße porn.

>>9735599
>he ate the brown one, get him his pills

>>9733464
Why do you think 0.999... is not representative of 0.9999...?

>>9735722
Not him but why do you think 0.999... is representing a final equivalence of absolutely infinite 9's of which there can be no greater amount of 9's, when you already know infinity as a final step is unachievable.

of course the obvious way of seeing 0.999... is just realizing there always exists another number greater than it by at least one more 9. Truly, there are an infinite amount of these numbers with more 9's that come between 0.999... and 1, and any attempt to imply invocation of the absolute final infinite'th value in this infinitely long set is reducing infinity to a finite real number and disregarding the intentionally incomprehensible nature of infinity by substituting an extremely truncated arbitrary value that truthfully is no less vague in execution than infinity itself already was: an otherwise entirely needless and facetious attempt at rationalizing infinity without actually making it any easier to understand, or a brainlet's trap of hubris.

>>9735738
Okay, I see where you're going with that. Approaching the situation that way would bring a person a back to where they started. Thank you for giving some insight.

>>9733594
>You write the 1 first, then write an infinite amount of zeros in front of it.

>>9733594

>>9733327
This is math, not retard-ville. Prove that .999...=/= 1. Show a number that is strictly between the two.

>>9737048
>Show a number that is strictly between the two.
(inf-1)/inf

>>9737061
=inf/inf

undefined

>>9737389
>undefined
why?