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/sci/ - Science & Math

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7364689 No.7364689[DELETED]  [Reply] [Original]

>me being a normalfag, not frequently on 4chan
>seen once post 0.99999999999... is not equal to 1
>but if 1/3 equals 0.3333333333... then 0.33333333...x3=0.9999999999... and 1/3x3 equals 1

so why people say it's wrong

>> No.7364702

>>7364689
Hello, normalfag. I am Autismo, lord of the shitposters. Welcome to the land of /sci/, just one vassal of my domain.

People say that 0.9999... is not 1 because they don't understand that decimal representations are nonunique. You're pretty much right modulo actually having a proof that is rigorous.

>> No.7364705

because then you could say that 0.000000.....1 is equal to 0, which is just pretty stupid

>> No.7364706

>>7364689
Unless you have a good internalization of infinity, you'll fuck this up.

>> No.7364708

>>7364689
Jellyfish will destroy the oceans and kill us all

>> No.7364711

>>7364705
Yeah, that is pretty stupid, because 0.0000...1 is not a sensible number. You can't have an infinite amount of something that ends with something else; you can always make the zeroes go farther and farther so the one never appears, but that's just the same as zero.

>> No.7364723

>>7364689
>so why people say it's wrong

Because you can't PROVE the existence of an equivalence relation with arithmetic. If f(x)=a and f(x)=b and a and b are distinct, then f is not a well defined function. You can "fix" it by imposing an equivalence relation but you can presuppose it already exists.

If you don't impose it then you have the hyperreals and nonstandard analysis (aka best analysis).

>> No.7364739

>>7364723
Why do you imply a is different from b? I thought the proof had to show a=b and I think that comparison method will prove it

>> No.7364751

>>7364689
People say it's wrong because they feel that a decimal that starts with "0." can't equal one. So they make up things like 0.000...1, or how it's just the limit so it can't be and all that good jazz. Completely disregarding that feelings don't matter and even if 0.000...1 wasn't complete nonsense there's no proof that 1-0.999... equals it. But hey, why be right if you can be edgy?

>> No.7364760

>>7364751
hahaha

>> No.7364771

Also if 0.999999.. is another number with it's own value you should be able express it as m/n where m and n integers. But as far as I know no such expression exists

>> No.7365202

>>7364723
Why do you think the result is different in non-standard analysis?

Have you not been paying attention to your classes?

>> No.7365261

>>7364711
You should clarify that you cannot have a well-ordered set with an ordinality of the form A+B for B zero or infinite and also have a well-defined last element.

>> No.7365288

>>7364705
no, because the ... necessarily represents a finite number of zeros. either that or the expression is nonsense.

>> No.7365305

>>7364689
It's just shitposting. You're basically right.

The decimal can be expressed like this: [math0.999... = \sum_{k=1}^{\infty} 9 \cdot 10^{-k}[/math], and so the difference between 0.999... and 1 is naught (as k goes to infinity).

>> No.7365306

>>7365305
Whoops, fucked up the tex.

<span class="math">0.999... = \sum_{k=1}^{\infty} 9 \cdot 10^{-k}[/spoiler]

There you go.

>> No.7365319

>>7364739
1.00000000...
0.99999999...

Digit one: 1 and 0 are different
Digit n: 0 and 9 are different

They are damn different strings

>> No.7365322

>>7365319
we're discussing numbers not strings me boi

>> No.7365324

>>7365288
>no, because the ... necessarily represents a finite number of zeros.
No it doesn't. That's the same as saying 0.99999... represents a finite amount of nines. Everyone agrees that 0.999...with a finite amount of trailing nines != 1. That isn't the debate here. The question is if .999... with infinitely many trailing nines is equal to 1, which it is, because the difference between them is 0.00000...1 which you said was nonsense. There literally is no difference between 1 and 0.999...

>> No.7365325

>>7365324
No idea what you saying. For great justice move 9.

>> No.7365331

>>7365325
I'm saying that when you subtract .999... from 1 the difference is .000...1, which you said was a nonsense expression. So quite literally the difference does not exist.

>> No.7365344

>>7365331
No, the difference is 0.
You can have 0.000...1 in other systems, and have that 0.999... = 1, thus their difference is 0.

>> No.7365356

>>7365344
Yeah, but there are two different interpretations of 0.000...1. One interpretation can mean a finite amount of zeros, which would make it a number with a magnitude. Another interpretation could be there are an infinite number of zero's, which has no magnitude and is equivalent to 0

>> No.7365363

>>7365356
The 0.0...1 I'm referring to is a number with an infinite amount of 0s, which is not equivalent to 0 (ie an infinitesimal).
What I'm saying is when this is the case, you still have that 0.999... =1.

>> No.7365379

>>7365363
The problem with using infinitesimals in this case is that you aren't using a well-defined means of comparing standard reals and infinitesimals. In nonstandard analysis this is often done with a standard part function taking every infinitesimal to the "nearest" standard real and every real to itself.

Taking the standard part of .0...01, even if it is defined, would still be 0.

>> No.7365382

>>7365331
no, there isn't. if there is a remainder of 10^-n where n is any integer, then you didn't have an infinite number of 9s to begin with and your premise is contradicted. by the archimedean property of the reals your .000...1 is equal to one such number or dne, with nonexistence following easily from the fact that .999... and 1 are reals.

>> No.7366132

Since 0.999...=1, then 1-0.999=0 there's no 0.000...1. I think those who don't get it have a distorted notion of infinity. Infinity has no value. To simplify you could say it's always growing. You'd get 0.000...1 only if you truncate the numbers of 9.

>> No.7366140

Its absolutely hilarious when people try to prove that 1 /= 0.999... or that 1 = 0.999... without ever actually referring to definition of numbers and infinite decimal expansions.

School screwed you over by introducing a concept (infinite decimal expansions) without giving the mathematical machinery to understand it.

>> No.7366262

>>7365379
No, what I'm saying is that the number <span class="math">0 + \epsilon \in \mathbb{R}^*[/spoiler], where <span class="math">\epsilon = 0.000...;...10...[/spoiler] is different from the number <span class="math">0 \in \mathbb{R}^*[/spoiler].

>> No.7366335

>>7364705
The point of the dots after 0.999... is to show that there is no final 9. 0.000... doesn't containt a 1 at the end, retard. Nice b8 tho

>> No.7366336

testing this

>> No.7366519

>>7366262
Oh, I agree of course then...

>> No.7366547

>>7366262
you know what you've written doesn't mean anything right

>> No.7366656

>>7366547
It does.

That's a valid decimal expansion for an infinitesimal, it's simply an infinite amount of 0s with a 1 at some infinite place, and then more 0s after.

>> No.7367917

>>7366656
You should have simply described it as a nonzero epsilon with zero standard part.

>> No.7368188

>>7365319
1/2 != .5
1/2 has a 1 and a 2 in it
.5 has a decimal and a 5 in it
They look different so they must not be equivalent

>> No.7368969

>>7366656
so close to them quints

>> No.7368995

>>7364689
It's because mathematics isn't based off physics.
Physics is based off mathematics.
If it was every time something was discovered the principles of mathematics would have to change.

So while it's true that absolutes either don't exist or are extremely rare in nature. Changing rules mathematics would be impractical.

Basically what I'm getting at is that saying 0.999.. isn't equal to 1. Is the same as saying the enobtainability of lightspeed voids the necessity of a definitive point at which light speed occurs. And instead of saying light speed we should say the infinitely increasing improbability of reaching the absolute speed of light.

>> No.7369011

>>7368995
What are you talking about

0.999... being equal to 1 has nothing to do with physics

0.999... equaling 1 is a purely mathematical fact.

>> No.7369082

>>7369011
Lets get rid of absolutes and instead use X.000... through Y.999... instead of using X as a definitive point.

>> No.7369084

>>7369082
What the shit are you even saying

>> No.7369099

>>7364689
0.999... is infinitely just out of reach
1 is definitive
they are not the same

If it was the same, it wouldn't infinitly trail with 9s implying there's an infinitely small separation between 1 and 1.999....

>> No.7369101

>>7369099
>they are not the same
They ARE the same.
It's just two different ways of writing the same thing

>> No.7369106

>>7369101
no it's not.
they are close to the same but they slightly different

>> No.7369110

>>7369101
imagine the universe is a jew.
if you had 0.999... shekels do you think they are going to call it a whole shekel?

>> No.7369112

>>7369101
That's called having a broken system you never fixed, but rather, hacked around.

>> No.7369221

>>7369106
Yes they are. Try taking 1 - .999...
You will get an infinite amount of 0s. There will never be a 1 at the end of the chain of decimals because there are infinite 9s.

If two numbers have a difference of zero then they are by definition equivalent.

>> No.7369230

>>7364771
> root 2
good luck expressing that as m/n kek

>> No.7369288

>>7369221
the difference isn't 0
It's 0.000...
if you're a million times larger then a super cluster looking at an atom from the rim of the universe.
it would look like the atoms next to it are overlapping. All 100billion of them sharing the same space. The distance between them is only 0.999... from your perspective.
Imagine the distance between quarks from that perspective.
imagine the wavelength at which a electron vibrates.
smaller still the distance it traveled in a single instant.

from your perspective sharing the same space as the entirety of the milky way.

but we know better. there are things infinitely smaller than an atom. And things infinitely smaller still.
All of which sharing the same space but never touching.

By definition they are not the same.
By natural law they are not the same.
Only through a 1 dimensional representation of the universe are they the same.

>> No.7369362

Lel Op listen to this
x = 0.9999...
10*x=9.9999...
if 1x=0.9999... then if you take that from 10x which = 9.9999... then you are left with 9 because you took away the 0.9999... duh. but 10x - 1x = 9x therefore if you divide that by nine you are left with one x which equals 1.
Be a fucking Maths Genis op.

>> No.7369392

>>7369288
0 followed by an infinite number of 0s is still 0.
At no point is there a 1 or any other nonzero number at the end of the trail of 0s.

>> No.7369412

>>7369288
>The distance between them is only 0.999... from your perspective.
No it would be some very small finite difference

>> No.7369485

>>7364689
YOU MOTHER FUCKERS ARE STUPID.

Lets say you dumb ass niggers are right and 0.999... = 1.
At what point does the infinitely decrementing integer become a real?
If your answer is, "the instant it became infinite". Then you are literally stating that the instant an integer becomes infinitely decremental. That it losses it's infinite property and becomes finite.
Now, mathematics is fucking broken because of niggers. And your equation is a paradox BECAUSE AN INFINITE DECREMENT CAN'T FUCKING HAPPEN NOW!

God, I hate you fucking people.

>> No.7369488

>>7369485
YOU MOTHER FUCKERS ARE STUPID.

Lets say you dumb ass niggers are right and 0.999... = 1.
At what point does the infinitely decrementing integer become a real?
If your answer is, "the instant it became infinite". Then you are literally stating that the instant an integer becomes infinitely decremental. That it losses it's infinite property and becomes finite.
Now, mathematics is fucking broken because of niggers. And your equation is a paradox BECAUSE AN INFINITE DECREMENT CAN'T FUCKING HAPPEN NOW!

God, I hate you fucking people.

>> No.7369491

>>7369488
YOU MOTHER FUCKERS ARE STUPID.

Lets say you dumb ass niggers are right and 0.999... = 1.
At what point does the infinitely decrementing integer become a real?
If your answer is, "the instant it became infinite". Then you are literally stating that the instant an integer becomes infinitely decremental. That it losses it's infinite property and becomes finite.
Now, mathematics is fucking broken because of niggers. And your equation is a paradox BECAUSE AN INFINITE DECREMENT CAN'T FUCKING HAPPEN NOW!

God, I hate you fucking people.

>> No.7369845

>>7369112
Do you consider different fractions representing the same number broken too?
What about a class of equivalence being represented by the different numbers?
What about the same vector space being represented by different bases?

Grow up.

>> No.7369864

>>7369491
>>7369488
>>7369485

mad cuz bad,
loud cuz dum

i suggest you git gud

>> No.7370089

>>7364708
Most sensible post in thread

>> No.7370101
File: 428 KB, 862x912, Iq-models-race.png [View same] [iqdb] [saucenao] [google]
7370101

>>7369488
>"the instant it became infinite"
.9* is a shorthand way of saying "the limit of the series 0.9 0.99 0.999 0.9999 etc"

To understand what this means you need more than babby calculus. You need at least the epsilon/delta formulation of limits, or preferably the topological version.

People who don't have this knowledge have no right to an opinion on the issue.

For example, one might expect that many negroes would have trouble with these concepts. Pic refers

>> No.7370103

>>7364705
0.000....1 = 10^-endless
This is considered 0 in every application you fucking idiot

>> No.7370108
File: 25 KB, 600x405, IQ_graph_racial -NVangd20060122.jpg [View same] [iqdb] [saucenao] [google]
7370108

>>7370101
inb4 racist
Pic should have been pic refers

>> No.7370112
File: 18 KB, 387x259, 643258.jpg [View same] [iqdb] [saucenao] [google]
7370112

>>7364705
>>7364711
>>7364751
>>7365331
>>7365344
>>7365356
>>7365363
>>7365379
>>7365382
>>7366132

MFW plebononic, junior college goin, pimply ass, neckbeard havin' astromerfs don't know what dx is and insist on saying 0.000...01

Goddammit you anons are stupid.

Tldr; 0.999999+dx=1
/ thread

>> No.7370115

>>7370101
>>7370108
Wow, it's true. These threads really are magnets for all the shitposters on /sci/.