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/sci/ - Science & Math


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9580334 No.9580334 [Reply] [Original] [archived.moe]

10 = 9.99999..

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

Explain to me why this does not disprove all of mathematics instead of prove that 10 = 9.999999.....?
If a vending machine want's $10 and I put in $9.99 i'm not getting my Pepsi.
Math is a scam.

>> No.9580366

Where the fuck did that x - x come from lil brainlet? What you do to the left must also be done to the right. You can't just fucking take stuff out without balancing it out on the other side

>> No.9580376

Let me reiterate on that, you cannot define 10*9.9999... the same as 99.99999... unless your number terminates or can at least be written as an irrational

>> No.9580384

>>9580366
>Where the fuck did that x - x come from lil brainlet? What you do to the left must also be done to the right. You can't just fucking take stuff out without balancing it out on the other side
Thats what I thought! This whole thing is bullshit.

>> No.9580387

>>9580366
>i think inf is a fixed number

>> No.9580392

>>9580384
>>9580366
samefag

>> No.9580407

>>9580366
he did do that, you fucking retard.

>> No.9580430
File: 59 KB, 1209x504, QzaUh7[1].png [View same] [iqdb] [saucenao] [google] [report]
9580430

>>9580392

>> No.9580436

QUICK RETARD FILTER QUESTION

x + x + x + x + ... (x times) = x^2

differentiate

1 + 1 + 1 + 1 + ... (x times) = 2x

x = 2x

How? If you don't answer why this can't be in 30 seconds your mom will die in her sleep tonight (counter blesses and protections don't work)

>> No.9580440

>>9580430
>i can use mspaint

>> No.9580444

>>9580436
sorry, your mom is a retard

but we will always have her pornhub videos to remember her by

>> No.9580586

>>9580436
Wtf, I don't know

>> No.9580599

>>9580444
>>9580586

Hope you said bye bye to mommy tonight, brainlets

>> No.9580621

>>9580436
Shit might be bait, idk, but it's because if given x+x+...+x (n times) = nx, we suppose that n is not a function of x.

But if it is, then we need to apply product rule to n(=x in your case), giving us
(LHS)' = n' * x + n * 1 = 2x = RHS

Sorry for bad formatting, it's 2am here; I'm phoneposting and lazy to latex

>> No.9580780

>>9580334
>If a vending machine want's $10 and I put in $9.99 i'm not getting my Pepsi.
What kind of pepsi is $10

>> No.9580788

>>9580334
Why do we have to have this low quality bait every day? Can't we at least get some high quality bait?

>> No.9580790

>>9580436
it'd be x^x, not x^2.

>> No.9580800

>>9580436
x+x+x... x times only equals x^2 for integer values of x. The functions aren't identical.

>> No.9581132

>>9580334
Take a course on Real Analysis, or read a book on it, and specially look at the construction of the Reals.

>> No.9581147

>>9581132
>tripfag's first real analysis course
You're very special, please teach us senpai.

>> No.9581157

>>9580334
a = 0.999...
10a = 9.999...
9a = 10a - a = 9
a = 1 = 0.999...

>> No.9581167

>>9580366
Jesus Christ how stupid can someone be

>> No.9581191
File: 761 KB, 1027x722, 1498490006987.jpg [View same] [iqdb] [saucenao] [google] [report]
9581191

Don't you guys ever get tired?

>> No.9581579

>>9581157
Infinity is unachievable. You'll never have anything but a finite amount of numbers in a repeating decimal. If you subtracted some significant amount from a to reduce it to 0.999
a=0.999
10a=9.990
9a = 10a-a = 8.991
a = 8.991÷9 = 0.999
You may then increment a by one more 9 and do the problem again, and continue doing this infinitely, and always get the same answer for a as you started with.

>> No.9581592

>>9580376
How exactly do you write something as an irrational?

>> No.9581601
File: 43 KB, 300x219, rene-descartes.jpg [View same] [iqdb] [saucenao] [google] [report]
9581601

>>9581167
I have been wondering this literally every day of my life

>> No.9581604

>>9581579
This.

Even if you have an infinite amount of 9's from 0.999... (which you can't, but w/e), multiplying it by 10 reduces the amount of 9's after the decimal. Subtract 0.999... and you're back to having an infinite amount of digits in the decimal where the last value within the infinite, not after the infinite, is 1.
[math]8.\underbrace{999 \cdots 1}_{\infty \text{ digits}}[/math]

>> No.9581613

you need to put in 9.(9)$

>> No.9581623

>>9581613
10 dollars
=
9 dollars,
9 dimes,
9 pennies,
9 shinnes,
9 dongols,
9 dennies,
9 zennys,
9 hinnys,
and
9 niggys

>> No.9581656

>>9581623
You're shortchanging me a niggy.

>> No.9581810

>>9581579
definition =/= construction

>> No.9581812

>>9581810
Construct the number 10

>> No.9581839

>>9581812
0 = {}
1 = {0} U 0
2 = {1] U 1
3 = {2} U 2
4 = {3} U 3
5 = {4} U 4
....
10 = {9} U 9

>> No.9581875

>>9581579

fucking reported

>> No.9581886

>>9581191
I thought I was on /a/ for a second and started to wonder why everyone was acting so retarded. I'm seriously starting to get the impression that /sci/ is actually one of the lower-IQ boards on this site.

>> No.9581902

>>9581886
>I'm seriously starting to get the impression that /sci/ is actually one of the lower-IQ boards on this site.
I don't think it is. But it is a board where people learn quickly not to post in any threads that cover their area of expertise, so there is a strong filter where the great majority of posts are by people who have no idea what they are talking about, even if there is quite a lot of actual knowledge present on the board.

>> No.9581924

>>9581839
Thanks for providing the methodology of being explicitly unable to construct infinity.

>> No.9581935
File: 12 KB, 394x379, squished wojak.png [View same] [iqdb] [saucenao] [google] [report]
9581935

>>9581924
>what is transfinite induction

>> No.9581962
File: 27 KB, 1399x147, germs dont exist.png [View same] [iqdb] [saucenao] [google] [report]
9581962

>> No.9582027

>>9581962
If you draw 0.9, 9, 9, 9 on a numberline and run out of room, you will have drawn a finite number of 9's...

Wikipedia is so retarded omg.

>> No.9582030

>>9581935
Transfinite oh is that how you cross the missing information gap between finite and infinity?

>> No.9582211

How is this board so retarded. If 0.(9) has an infinite number of nines after the comma then it must be 1 by definition since it's a real number because it's infinitively close to 1. If it is infinitively close then there can be no numbers in between 0.(9) and 1 which means they are the same number. If it isn't then it wasn't infinite number of nines to begin with.

>> No.9582238

[math]
x= \frac{1}{10} \\
0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\
0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\
0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1
[/math]

>> No.9582372

>>9582211
There is no such thing as "infinitely close". That is literal gibberish.

The closest anything can be to another thing is a plank length and that is definitely finite.

Seriously you can't even begin to rationally describe what "infinitely close" means.

>> No.9582377
File: 162 KB, 329x353, 1509443183555.gif [View same] [iqdb] [saucenao] [google] [report]
9582377

>>9580334
when will /sci/ be able to transcend numberphile tier clickbait?

>> No.9582378

>>9582372
1/inf=0

protip: same as your iq

>> No.9582386

>>9582027
its obvious that wiki leaves out detail.
no where did they claim the proof is based on you being physically incapable of drawing more distinct lines

>> No.9582390

>>9582372
infinitely close is the distance from an open set to a limit point of that open set.

>> No.9582393

>>9582372

You can actually.
Suppose we have x and y such that y > x. y will be infinitively close if y < a where a is any number that is bigger than x. If y < a is true for any valid a then y is infinitively close to x.

>> No.9582399

>>9582393
>>>9582372
>
>You can actually.
>Suppose we have x and y such that y > x. y will be infinitively close if y < a where a is any number that is bigger than x. If y < a is true for any valid a then y is infinitively close to x.
I meant y >= x.

>> No.9582416

>>9582238
This assumes infinity is a quantity that can be obtained as well as it being a number since it relies on [math]1-x^{\infty}[/math], which means we can just as easily rewrite as [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] where the infinite partial sum is 0 and irrelevant to the sum total meaning all summable work occurred before n=infinity, yet any test of real n doesn't provide an infinite amount of 9's.

Oopsie poopsie!

>> No.9582429

>>9582416
It actually relies on [math]1-x^{\infty +1}[/math] since [math](1-x)(1 + x + x^2 + x^3) = 1-x^4[/math], so the end of the sequence at [math]\cdots + x^{\infty}[/math] means altogether it's [math]1-x^{\infty +1}[/math], which directly invokes the undefinable vagueness property of accuracy loss by having used infinity when it doesn't even exist, since infinity+1 is not different from infinity by itself. In the end, you actually lose a value.

>> No.9582434

>>9582429
Rather you gained a value.

>> No.9582441

>>9582429
>>9582434
ACTUALLY the end of the sequence is [math]\cdots -x^{\infty} + x^{\infty} \big)[/math] and that value is undefined, so you either only get [math]x^{\mathbb{R}}[/math] as a maximum to the sequence or the entire sequence becomes invalidated as undefined. Either way, no longer infinite.

>> No.9582449
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9582449

>>9582378
[math]\frac{\mathbb{R}}{\infty} = 0[/math] so thats not saying much. In relation to infinity, 1 is infinitely close to a googol, cause not even 1 with a googolplex googols of zeros after it is anywhere close to infinity.

Great methodology.

>> No.9582474
File: 73 KB, 798x798, smilelaugh.jpg [View same] [iqdb] [saucenao] [google] [report]
9582474

>>9582449
In relation to infinity, all numbers have the same value of 0. 1 is no closer to infinity than a billion.
Therefore because infinity, 1 = 1,000,000,000 and also any [math]r \in \mathbb{R} = \text{ any other } r \in \mathbb{R}[/math]

thanks, infinity. Numbers no longer have value and cannot be ordered.

>> No.9582482

Infinity needs to be redefined as the only number you shouldn't analyze cause doing so would prove it wrong.

Infinity should be redefined as the holocaust.

>> No.9582484

>>9582482
but then infinity would only have a value of 6 million.

>> No.9582486

>>9582474
finite doesn't push infinite around

is this surprising to you? baka

>> No.9582488
File: 32 KB, 312x342, 1508745104360.jpg [View same] [iqdb] [saucenao] [google] [report]
9582488

>>9582484
>but then infinity would only have a value of 250,000
ftfy

>> No.9582489

Wtf is wrong with this board. It's supposed to be science and math but it's mathlets everywhere.

>> No.9582490

>>9582482
>redefined
from what?

>> No.9582494

>>9582486
A number theory which includes infinity can no longer be well ordered. You want to make sense of the 9's in 0.999... being infinitely close to 1, that doesn't mean much when 1 is then infinitely close to a billion.

>> No.9582509

>>9582494
>includes infinity
it's kept separate from R
lrn2read

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

>> No.9582516

>>9582509
Where the fuck did the post say infinity had to be a real number.

Learn to read retard.

>> No.9582518

>>9580334
TRY PUTTING $9.99999999... INTO THE VENDING MACHINE IDIOT

>> No.9582539

>>9581924
∃x( { } ∈ x ∧ ∀u[u ∈ x → ∃y(y ∈ x ∧ u ∈ y ∧ ∀v[v ∈ u → v ∈ y])])

First encountered in axiomatic set theory.

>>9582372
Usually by using this phrase they mean lim Δx→0 [ f(x) = x + Δx ] or similar notion by context.

First encountered in calculus.

>>thread

In the construction of the reals, 1 ≡ seg≤(Q,1). Any set bounded from above at 1 with a proper initial segment and no greatest element is equal to 1 ∈ R by definition. One example of such at set would be A = { 1 - 1/n : n ∈ a+ }.

First encountered in real analysis.

>> No.9582584

>>9582516
https://www.tfd.com/includes

>> No.9582588
File: 14 KB, 300x168, 10.jpg [View same] [iqdb] [saucenao] [google] [report]
9582588

>>9582518
people do it erry day

>> No.9582596

>>9582584
>A number theory which includes infinity can no longer be well ordered
A NUMBER THEORY that ALLOWS infinity is worthless.

Nothing about the post said real numbers.

You actually need to learn how to read.

>> No.9582603
File: 73 KB, 1024x1024, bait 0.9.png [View same] [iqdb] [saucenao] [google] [report]
9582603

>>9580334

>> No.9582608

>>9582596
>my number theory doesn't include numbers

ok. sounds relaxing.

>> No.9582612

>>9582494
Construct the triangle of points ABC
A = (0 , 0)
B = (1,000,000,000 , 0)
C= (500,000,000, [math]\sum_{n=1}^{\infty}n[/math])

Our point of view is point C

As C.y goes off to infinity, the lines CA and CB become parallel and overlap. Relative to C, A and B are infinitely close to each other. Therefore 0 = 1,000,000,000

Are we sure we really want to use "infinitely close" to describe a relationshio between 0.999... and 1? Cause it seems like using that methodology, any number can then be equal to any other number.

>> No.9582621

>>9582612
0.999 repeating is greater than any number less than 1. 1 isn't greater than any number less than 2. So we can very easily see that 1 cannot be infinitively close to 2 but 0.999 can be infinitively close to 1.

>> No.9582622

>>9582612
Again, you need to read a book on Real Analysis for proper answers.

>> No.9582627
File: 86 KB, 384x313, s4dTtBy.jpg [View same] [iqdb] [saucenao] [google] [report]
9582627

>>9582608
bro you might be retarded.

>> No.9582634

>>9582621
Relative to infinity there is zero distance between 1 and a billion. I'm not sure how you failed to understand that, it's directly alloted for by [math]\frac{\mathbb{R}}{\infty} = 0 [/math]. No number rationally exists between 1 and a billion. They are infinitely close to each other.

You might want to ask yourself who's fault it is that you believe so strongly in a fallacy that you will sooner ignore and question the validity of PROOF than change your mind.

>> No.9582646

>>9582634
Except they aren't because there are infinite number of numbers between 1 and 1 billion just like between 1 billion amd infinity.

>> No.9582648

>>9582646
Right, but that doesn't matter. There are also an infinite amount of numbers between 0 and 1, but you're not treating them with unique identities there are you?

Your arguement is 0.999... = 1 because there is no positive value to add to 0.999... that will equate 1. The argument in total is that 1 = 1 billion because there is no positive value to add to 1 that will equate 1 billion. Both 1 and 1 billion share the same value identity of 0.

>> No.9582649

>>9582634
>zero distance between 1 and a billion
can I have my $1 bn now?

>> No.9582652

>>9582649
As soon as there is infinite money.

Unfortunately infinity doesn't exist.

Even if you did get the money though, it wouldn't actually be worth anything.

>> No.9582653

>>9582648
No. The argument is that there is no real number between 1 and 0.999 repeating vut there is an infinite reals between 1 and 2.

>> No.9582656

>>9582653
There exists no number between 1 and 1 billion. They are infinitely close to each other.

Maybe a third time is the charm?
Hello, anybody in there?

>> No.9582657

>>9582656


>>9582656
>>>9582653 (You)
>There exists no number between 1 and 1 billion. They are infinitely close to each other.
>
>Maybe a third time is the charm?
>Hello, anybody in there?
Okay what. Did you have a stroke there?

>> No.9582672

>>9582657
Maybe a fourth time will do the trick.

0.999... < r < 1
You believe no number r exists, that the value identity of r must then not be one of a positive number, but instead 0. R itself isn't "0", just that, because you believe there is no r here, the r of the problem has zero relevance.

Now, for 1 < r < 1,000,000,000 ; no r exists here either. There is no positive value r to add to 1, so the valuable identity of r is 0.

1 = 1,000,000,000

>> No.9582677

>>9582652
there is, infinite far away

>> No.9582680

>>9582672
Sorry, you're losing the other guy, and me.

There is no Real Number r so that 0.999... < r < 1.

There exists a Real Number r so that 1 < r < 2. For example, 1.5.

>> No.9582683

>>9582672
Wtf are you talking about
Why would r be 0 here in either case? Who claimed that?

>> No.9582693

>>9582680
You can't prove 1.5 exists as a number between 1 and 2.

You allow infinity to exist, then all real numbers relative to infinity are infinitely close to each other.

• [math]\frac{\mathbb{R}}{\infty} = 0[/math] means all real numbers have zero value and all real numbers equal each other.
• 1 might be less than 5 relative to 10 since 1 is (10-1):9 away and 5 is (10-5):5 away, but 1 is the same number as 5 relative to infinity since 1 is (inf-1):inf and 5 is (inf-5):inf

f-fifth time is the charm...

>> No.9582697

>>9582693
>You can't prove 1.5 exists as a number between 1 and 2.
lolwut

>You allow infinity to exist, then all real numbers relative to infinity are infinitely close to each other.
Ok, but I thought we were talking about the Reals, and infinity is not a Real Number. Not sure what you're on about here, but you're completely off-base. No one else is making silly arguments like "well, compared to 1 billion, 0 and 1 are really close". No one is invoking infinity either.

>> No.9582700

>>9582697
You aren't invoking infinity my claiming 0.999... has an infinite amount of 9's or that it is infinitely close to 1 or that there are infinite numbers between 0 and 1?
Really?

>> No.9582702

>>9582693
1 is 1 less than 2 no matter if you include infinity or not. Why would you relate anything here to infinity?

>> No.9582705

>>9582702
2 is just a made up number you invented to pretend there exist values between 1 and 1 billion.

>> No.9582706

>>9580366
Watch who you call brainlet lol

>> No.9582707

>>9582700
Not really, no.

Generally in proper mathematical circles, 0.999... (repeating) can be identified in various ways. One can think of it as a decimal expansion. A decimal expansion is a function f : N -> {0, 1, ..., 9}
In this case, the decimal expansion is simply the constant function f(x) = 9

No need for a value of infinity here.

Then, we can use standard calculus limits and the standard construction of the Reals. No infinity values here either.

>> No.9582709

>>9582700

Infinity isn't a part of real numbers. There is an infinite number of real numbers but that doesn't say that infinity is one of them.

That's like saying that in a set {2, 3} 2 is 1 less than 3 so 1 is involved in the set.

>> No.9582713

>>9582707
I'm glad you're agreeing there are only a finite amount of 9's in 0.999...

>> No.9582714

>>9580780
It also works with 0.9999999

>> No.9582715

>>9582713
I didn't say that. I said that I didn't need the number "infinity". I do need an infinite set, such as Natural Numbers. However, Natural Numbers does not contain the value "infinity".

>> No.9582716

>>9582709
Guess that means you can't have an infinitr amount of 9's in 0.999... and must therefore only be able to have a finite amount of 9's.

>> No.9582717

>>9582705


Either way there is no real number that is greater than 0.999 repeating but lower than 1. There are quite a few real numbers that are greater than 1 but lower than 1 billion.

>> No.9582718

>>9580436
Why are anons struggling e
With this? There diverative of x^2 is notbequal to x^2

>> No.9582719

>>9582716
How does that follow?

>> No.9582722

>>9582716
In other words, there are an infinite number of Natural Numbers, but "infinity" is not a Natural Number. That's the distinction that I'm trying to draw here.

In the decimal expansion 0.999... (repeating), there are an infinite number of '9's, just like there are an infinite number of Natural Numbers. However, infinity is still not a Natural Number, and it's still not a Real Number.

>> No.9582728

>>9582717
There is literally no real number you knob gobbler.

There can only be a finite amount of 9's in the number you pretend to hope has an infinite amount of 9's, and there will always exist a real number between it and 1 that in the very least just has one more 9 in it. Thats the fact.
You presume one value equals the other because you think it is touching it, but one planck length touches another yet these are not assumed to be the same planck length. No value of distance can exist between two touching planck lengths.

>> No.9582730

>>9582728
Planck length has no meaning here. And they aren't touching. There are no numbers between them so they must be one and the same number.

>> No.9582733

>>9582728
>planck length
pics or it didn't happen

>> No.9582734

>>9582722
So you argue that there are infinite real numbers and none of them equal infinity, and you argue there are an infinite amount of 9's in 0.999..., yet also aren't intelligent enough to rationalize that the infinite 9's are relateable to infinite numbers, and since infinity is not a real number, there does not exist a real number 0.999... with infinite 9's.

Your argument is that you are literally retarded?
Bravo.

>> No.9582736

>>9582734

That is actually true. The number of nines in 0.999 repeating is infinite therefore it's not a real number but 0.999 repeating itself is a real number.

There are no contradictions here.

>> No.9582737

>>9582734
Take some intro college math courses. Again, it should be pretty easy to see:

The size of the set N, the set of Natural Numbers, does not equal any Natural Number. In colloquial terms, the set has infinite size.

N does not contain the element "infinity".

This should all be amazingly straightforward and obvious.

One way to define a sequence of infinite '9's is simply a function from naturals to digits, f, where f is a constant function, f(x) = 9.

This is all quite elementary, obvious, and covered in low-level college courses, i.e. Real Analysis.

>> No.9582739

>>9582736
No, the point was there exists no repeating decimal with infinite repetition. Not 0.333...
Not 0.666...
Not 0.999...
You can't have infinite.

Are you saying 0.333... isn't a real number too?

>> No.9582740

>>9582734
Another example is square root of 2. Since square root of 2 is irrational then decimal expansion has an infinite number of digits. Square root of 1 is still a real number.

>> No.9582743

>>9582737
Right so i just bent you over and fucked you stupid, i don't care what you have to say. You dont need to pretend you're smart around me baby, if you didn't want to get fucked you would have been smart from the get go.

>> No.9582745

>>9582739
>You can't have infinite.
Why not?

>Are you saying 0.333... isn't a real number too?
This is partially a terminology and notation issue. If that was in a typical math textbook or paper, it would be interpreted in a way to be equal a Real Number, the Real Number which is equal to 1/3.

>>9582743
I'm not sure where this hostility is coming from. Have a good night!

>> No.9582746

>>9582739
You can very easily show a number with infinitively repeating digits.
a is equal to the infinite sum of 9/10^n for n from 1 to infinity.
a is a real number with infinite decimal repeating expansion.

>> No.9582749

>>9582740
Irrationality doesnt provide for infinite existing or not. You could have just said pi instead, but wouldnt change the fact that no one could ever need to use pi accurate to more than 284 decimal places.

>> No.9582750

>>9582749
This is a discussion about math, not engineering.

>> No.9582751

>>9582749
How is that relevant? Pi still has an infinite decimal expansion.

>> No.9582753

>>9582750
This is a discussion about math, not fantasy fucking useless bullshit.

>> No.9582754

>>9582753
>This is a discussion about math, not fantasy fucking useless bullshit.
They're often the same thing.

>> No.9582758

>>9582746
If you assume the limit is never reached, there will only ever be a finite amount of 9's in a.

If you assume the linit can be reached, you get the partial sum of 0 which is irrelevant to the total sum, therefore reaching infinity was too much. Backtrack to any sum before n=infinity, and you only have a finite amount of 9's.

No infinite repetition.

>> No.9582761

>>9582758
It's not a process. It's not a limit. It's a function from Naturals to Digits, which is a particular kind of function from Naturals to Naturals. Do you have a philosophical problem with functions from Naturals to Naturals, such as f(x) = x+2?

>> No.9582762

>>9582758

This is high school level math. You might be retarded. Or an edgy middle schooler.

>> No.9582769

There are infinite real numbers, and none of them equal infinity.

You can map all the number integers from 0 to arbitrary greatness as real numbers between 0 and 1

Because infinity doesn't exist in the real numbers, all the real numbers between 0 and 1 are not infinite, and are perfectly mappable to all the real number integers between 0 and arbitrary greateness

There are a finite amount of 9's in 0.9repeating, such that a number 0.0repeating1 added to it sums 1.

Too bad infinity isn't a real number...

>> No.9582782

>>9582769
For posterity, the first line should read "there are unlimited real numbers and none of them equal infinity"

>> No.9583041

>>9582769
>There are a finite amount of 9's in 0.9repeating,
Wrong.

>such that a number 0.0repeating1
No such real number.

>> No.9583123 [DELETED] 

>>9583041
Does infinity exist in the real numbers?
That means only real numbers exist between 0 and non-inclusive infinity

If you map the real numbers between 0 and infinity, non-inclusive of infinity, between 0 and 1, non-inclusive of 1, becuse you cannot reach infinity means you cannot reach 1. Because only all real numbers exist between 0 and non-inclusive infinity, only all real numbers exist between 0 and non-inclusive, there the largest real number greater than 0 and less than 1 is 0.999...

0.999... =/= 1

>> No.9583127

>>9583041
Does infinity exist in the real numbers?
That means only real numbers exist between 0 and non-inclusive infinity

If you map the real numbers between 0 and infinity (non-inclusive of infinity), between 0 and 1 (non-inclusive of 1, sinxe you cannot reach infinity means you cannot reach 1. Because only all real numbers exist between 0 and non-inclusive infinity, only all real numbers exist between 0 and non-inclusive 1, therefore the largest real number greater than 0 and less than 1 is 0.999...

0.999... =/= 1

>> No.9583136

>>9583127
0.999 repeating isn't infinity and is a real number you brainlet

>> No.9583141

>>9583136
0.999... doesn't have an infinite amount of 9's, right. Thats what i said.

>> No.9583151

>>9583127
>therefore the largest real number greater than 0 and less than 1 is 0.999...
That doesn't follow from what you're saying. Why does it matter if "only all real numbers" exist in [0,1)? Do you think that infinitely repeating decimals aren't real? The interval has no greatest element, just like [math][0,\infty)[/math] has no greatest element. For any finite sequence of 9's, you can add any number at the end to get something between it and one.

>> No.9583154

>>9582758
>a is equal to an infinite sum
>nuh uh

>> No.9583164

>>9583141
What do being infinite and having an infinite decimal expansion have to do with each other?

>> No.9583169

>>9583151
Im saying all the numbers between 0 and infinity can me mapped between 0 and 1. That there exist an equal number of analogues between 0 and 1 as 0 and infinity.
This means that since there is no way to increment to infinity, there exists no analog as the increment from 0 to 1. There will ony ever exist a largest real number number ahead of infinity, and thus can only exist the same largest real number of decimals between 0 and 1.

I'm not aure how many more different ways I can rephrase it, so if you didn't understand it this time all I can do is award you with stupid nigger of the year.

>> No.9583172

>>9580334
You put 10 = 9.999 at the beginning so you get x=9.9999

The whole thing is bogus. I don't know what the other anons are even discussing about.

>> No.9583186

>>9583169
A nice function that can map 0 to 1 to 0 to infinity is f(x) = 1 / (1 - x) - 1
Of course it only approaches infinity as x goes to 1.

>> No.9583188

>>9583172

10 = 9.999 isn't part of the argument but the title more or less. It's the reason there are 2 line breaks after it.

>> No.9583200

>>9583172
x= 0.999...
10x = 9.999...

[math]\infty x = \bar{9}[/math] (a real number)
[math] \bar{9} = \infty[/math]
Uh oh looks like infinity fags fucked up again.

>> No.9583250

[math]\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 and 1} \\ 0 \rightarrow 1 = \overbrace{\underbrace{0.9, 0.99, 0.999, 0.9999, \cdots}_{\infty \text{ elements of } \mathbb{R}}, \underbrace{1}_{\text{not in }\mathbb{R}}}^{\text{all possible elements}}[/math]

>> No.9583283

>>9583250
Mapped between 0.9 and 1

>> No.9583285

>>9583250
so 1 is not a real number? huh, ok

>> No.9583292

>>9583285
1 is the mapped analog to infinity, so between the mapped analogs of all real numbers between 0 and infinity, 1 isn't included in the real subdivisions between 0 and 1.

Thanks for knowing what mapped means brainlet.

>> No.9583298

>>9583292
sure it isn't included in the subdivisions between 0 and 1, but 1 is still a real number, your analogy is shit

>calling others brainlet while trying to "prove" this bullshit
HAH

>> No.9583306

>>9583298
I'm not arguing about whether 1 is a real number and you just admitted to understanding 1 isnt mappable as a real number from 0 to infinity mapped as 0 to 1 so what the fuck ever retard, continue crying about shit that doesnt matter while admitting i am right.

>> No.9583323

>>9580334
You're considering x=9.99999... Irrational

In the real world stuff usually costs in 9.99

So if you consider that it is rational then the math checks out

>> No.9583330

>>9583250
By the map, if 0.999... is assumed to equal 1, then there also must exist a real number assumed to equal infinity, thus infinity is a real number.
However since there is no way to increment to the real number infinity, there is also is no way to increment to 1 from 0.999...

0.999... =/= 1

>> No.9583417

So once again. By definition, there are no two real numbers that are infinitely close and not equal. That's because if two real numbers are not equal then you can always find a real number that is in between the two.

Now, let's suppose we have some number [math]k[/math] such that [math]0.\bar{9} < k < 1[/math]
If such [math]k[/math] exists then [math]0.\bar{9} \neq 1[/math]
The problem is that no such real [math]k[/math] exists.

Let [math]f(x) = \sum_{n = 1}^{x}\frac{9}{10^n}[/math]
For any real [math]k[/math] such that [math]k < 1[/math] you can find [math]x[/math] such that [math]f(x) > k[/math]

Because there is no real [math]k[/math] there are no real numbers between [math]0.\bar{9}[/math] and [math]1[/math]
Because there are no real numbers between [math]0.\bar{9}[/math] and [math]1[/math] that means they must be equal.

>> No.9583426

>>9582612
>using commas to clarify large numbers while also using commas to seperate components
must be american
learn to write 1000000 instead of 1,000,000 please

>> No.9583440

>>9583426

Or even 10^6 for ease of reading

>> No.9583444
File: 9 KB, 211x239, 1513971000563.png [View same] [iqdb] [saucenao] [google] [report]
9583444

>>9583417
The irony of your post coming directly after a post that explained why assuming 0.999... = 1 is retarded by using the same logic you used.

>> No.9583456

>>9583444

>if 0.999... is assumed to equal 1, then there also must exist a real number assumed to equal infinity

How does that follow?

>> No.9583459

>>9583456
>>9583250

>> No.9583460

>>9583444

And nowhere I said anything about infinity.

>> No.9583469
File: 492 KB, 1080x1080, 2018-03-13 13.57.03.png [View same] [iqdb] [saucenao] [google] [report]
9583469

>>9583460
Right here

>> No.9583472

>>9583444

You could start by pointing out flaws in my proof.

>> No.9583474

>>9580436
Am i a brainlet? Still stuck on this

x + x + x + x +... (x times) = x(1 + 1 + 1 + 1 +..)
d/dx = (1+1+1+1+...) = x

So x+x+x+x+... cannot be x^2.
Then what is it?

>> No.9583476

>>9583469
Infinitively close isn't infinity. And I mentioned it once explaining how real numbers and that was it.

>> No.9583478

>>9583472
You could start by paying attention to the proof before yours and realizing it is more rigorous. Its not my job to correct you. The necessary information exists, it's your job to learn it.

>> No.9583481

>>9583478
>More rigorous
I'm convinced you aren't a brainlet and just pretending to be retarded.

>> No.9583483

>>9583474
You can only do d/dx ax = a when a is constant. In this case a = 1 + 1 + 1 + 1 + ... x times so it depends on x so it's not constant therefore you can't do that.

>> No.9583484
File: 94 KB, 866x900, 1512784797225.png [View same] [iqdb] [saucenao] [google] [report]
9583484

>>9583481
Right, thats why you want me to prove you wrong instead of you yourself being able to prove me wrong.

I'm the brainlet. Right. Okay buddy. Ahuh. Sure.

Heres one more picture of (You).

>> No.9583486

>>9583484

I posted a proof but you refuse to point out the flaws in it. Not my fault.

>> No.9583489
File: 16 KB, 498x467, 1512340128839.png [View same] [iqdb] [saucenao] [google] [report]
9583489

>>9583486
You refused to acknowledge the proof posted before your own. Not my fault.
Here's another (You)

>> No.9583493

>>9583489

What proof even

>> No.9583505

>>9583493
Exactly my point. You refuse to acknowledge it. Here's an existential question for you. Are you deliberately refusing to acknowledge it, or are you only refusing to acknowledge it because I dictated you couldn't?

>> No.9583520

>>9583505

I might as well say that you never presented any proof and that you are refusing to support your position and address proofs.

>> No.9583524

>>9583520
You may as well, I dictate your life after all because I am your God, and I said you wont acknowledge proof so you wont, for I as God my word is truth.
And also so is my proof :^)

>> No.9583527

>>9583474
>>9583483
think i figured i out in another way.
f(x) = x+x+x+x+... = x^2 only when x is an integer.
which means you cant differentiate f(x)

>> No.9583616

>>9581601
Semi-underrated

>> No.9583653

>>9580334
9.99=/=9.99...=10

>> No.9583695

>>9580334
>>9580366
>>9580384

State of /sci/

>> No.9583725

>>9583653
>9.999...=10
[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 allowing a real number to be equal to infinity.

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 0.9 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 flawed assumptions about the construction of a repeating decimal extended from a flawed interpretation of infinity.

>> No.9583784

The difference between 1 and the largest real number is infinitely smaller than the difference between the largest real number and infinity. Relative to infinity, all numbers are the same number: 0

>> No.9583787

>>9583725
I applaud your LaTeX skills, but I hope you realize you have written complete mathematical nonsense here. That's an unusual combination to see in the wild, to be sure.

>> No.9583793

>>9583784
The number system where only 0 and a single non-zero value exist is binary, but even still binary can represent numbers while infinity cannot.

>> No.9583795

>>9583787
It's fact, sorry bro. If you're too retarded to learn facts then you're better off no talking to anyone ever again.

>> No.9583814

>>9583725
>>9583787
8/10 troll

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