Discuss.

>>729028098
It is.

>>729028191
/thread

>>729028098
it's not 0 either

File: 1489871810636.jpg (33KB, 500x385px)

33KB, 500x385px

>>729028098
Technically, it is

>>729028098
It is as close to one as you can possibly get.

>>729028309
no it is exactly 1

>>729028191
Yup.
NEXT

>>729028309
>It is as close to one as you can possibly get without being one.
One is closer to one. So FTFY.

1/3 =.3 repeating
.3 repeating x3 = .9 repeating
.9 repeating = 1

There's nothing to discuss here except "you're wrong."

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

0.999... = 1 now fuck off

>>729028098

X =.999
10x = 9.999
10x = 9 + x
9x = 9
X = 1
Science yo.

>>729028564
>10x - x = 9.999
>9x = 9
nigga wut?
it would be 9x = 9.999...
dumbfuck

>>729028098
If you want anyone to take you seriously, you have to define what "1" is, then build up to defining the real numbers and their decimal representations. And if you do all that (which I have), then you will figure out that .999...=1.

>>729028455
False citation.

>>729028564
X= .99
10x= 9.9
10x-x=9.9-.9
9x=9
X=1

So.9 =1 too?

>>729028753
>Purposely misquoting his post

wowee

>>729028098
Well, it can be said at least that the geometric progression:
9/10 + 9/100 + 9/1000 + ...

Converges to 1

must not let flat earthers take over the maths too!

>>729028857
>9.9-0.99=9

>>729028098
1 is 1.0. Not more and not less. So 0,99999.... is not 1. If it would be 1 than 99 would be 100, which it is obviously not

>>729028982
Here's the proof:
The sum of a infinite series of the form
1 + x + x^2 + x^3 + ...
equals 1/(1-x) as long as |x|<1

Now, say that x = 1/10, then:

1 + (1/10) + (1/10)^2 + ... = 1/(1-(1/10))

Multiply both sides by 9 and you have

9 + 9(1/10) + 9(1/10)^2 + ... = 9/(1-1/10)

Simplify the fraction on the right hand side by multiplying by 10/10:

9 + 9(1/10) + 9(1/10)^2 + ... = 90/(10-1)

Pass the 9 to the other side and simplify:

9/10 + (9/10)^2 + ... = 10 - 9

Hence

9/10 + (9/10)^2 + ... = 1

>>729028098
I'm guessing you're one of those Philosophy majors...or a political science major.

You know; the studies that don't matter.

>>729028098
.9 repeating is a geometric series equivalent to (sigma) =.9 * (1/10)^n

In a geometric series with R > 1, the sum can be found using the formula A/(1-r). In this case, a =.9. 1 - 0.1 = 0.9, which makes the summation equation a/(1-r) equal to 0.9/0.9,

Therefore, according to calculus, 0.99 repeating = 1.

>>729028098
In any mathematical system where 0.999... =1 means that 0.999...98=.999...97=0.999.96=0.999...95, etc, etc., ad infinitum

The entire number system breaks down because all numbers exactly equal each other.

>>729029843
Proof?
>no proof.

>>729029942
I wrote down one, just scroll up

>>729029942
If you think I'm going to spend the time explaining how an infinite geometric series works over /b/, you must be clinically retarded.

If you're legitimately curious about it and want to know more, there are a shitload of good websites you can check out. I think there's even a khan academy video about it. It's actually pretty interesting if you take the time to learn.

There is no last number.

0.999... is an increasing number that gets closer and closer to, but never reaches, 1.

>>729028098
.099... is a real number that is the same as the real number 1, since it is greater than every rational number strictly less than 1. (This follows from the definition of a dedekind cut.) Another way to put this is, there is no x a subset of 1 such that x is not also a subset of .999... therefore 1 is not strictly greater than it.

However, it is not equal to the natural number 1, which is just {{}}; this would violate extensionality.

>>729030080
>>729029474
OK, I'll bite.
Now prove that the sum of an infinite series of the form 1+x+x^2+x^3+... equals 1/(1-x) as long as |x|>1.

>>729030419
>0.099... is greater than every rational number less than 1
It's not even greater than 0.5 kek

try again

thoumst mom is a gay

>>729030605
Missed a decimal place on mobile. eat a log of shit out of my ass.

>>729030596
Ok gimme a minute

>>729028098
0.99999999 is infinitely far away from 1.0

>>729030739
>makes basic errors in his attempt at a troll post
>immediately rages when called out

try harder.

Literally it is not it holds its own numerical value but in a everyday sense, it's 1.

>>729030596
And then prove that it is not also the case between 0.999....99 and .0999...98.

Because both are of "equal distance" on any number line. Meaning if 0.999... = 1 then all other numbers equally distant from each other ALSO equal each other. Which then collapses the entire numbering system as all numbers equal each other.
Go ahead, prove me wrong.

>>729030910
It's not? if 1/3 = 0.333... => 3/3 = 0.999... since 3/3=1 => 1=0.999...

It's not

That only works if you pass to limit

>>729028098
Look morons...
.9999...=x. Multiply by 10
9.9999...=10x subtract from each side
9= 9x divide by 9
1= x ergo
1=.9999... By definition of terms.

58 yr old Boomer here. You fuckers didn't learn shit in school, got participation trophies, are addicted to technology, have short attention spans. Just kill yourselves already.

>>729030966
You should learn the definition of a decimal representation before posting idiotic shit like this.

>>729028982

>Converges

>>729030837
Ok you did succeed in rustling me slightly, but my post is not a troll post, it's grounded in accepted principles of classical set theory

DOES not = x.

Otherwise move along nothing to see here.

>>729030596
>>729029474
Here:
Suppose that x is a number that could be either complex or real

Consider the finite series

1 + x + x^2 + x^3 + ... + x^n

Store the entire sum into a number, namely s_n:

s_n = 1 + x + x^2 + x^3 + ... + x^n (*)

Multiply both sides by the same x:

x(s_n) = x + x^2 + x^3 + ... + x^n + x^(n+1) (**)

Subtract (*) from (**):

(1-x)s_n = 1 + x + x^2 + x^3 + ... + x^n - (x + x^2 + x^3 + ... + x^n + x^(n+1))

A lot of terms will cancel out in this sum. In fact, only 1 and x^(n+1) will survive because the appear in either (*) or (**) once. Hence:

(1-x)s_n = 1 - x^(n+1)

Now, since dividing by zero makes no sense, we have to admit that x is not equal to 1. If that is the case then:

s_n = ( 1 - x^(n-1) ) / (1-x)

Now, that is the sum of a finite geometric progression. The sum of a infinite series however, is defined as the LIMIT of such sum as n tends to infinity. In this case the limit is:

lim s_n = lim(1 - x^(n-1)) / lim(1-x)

I used the fact that the limit of a quotient is the quotient of limits as long as the denominator isn't zero

Now,

lim s_n = (1 - lim(x^(n+1))) / (1-x) (***)

(Subtraction of a limit is the limit of a subtraction and 1-x is continuous on x not being 1)

From (***), you can already see that the limit will only exist if x^(n+1) gets smaller as n gets big, which only happens for |x|<1. Eventually, as n goes to infinity, x^(n+1) goes to zero

Thus:

s = lim(s_n) = 1/(1-x)

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>>729031235
you would have to subtract 9x not 9 in order to get just x.

Fucking get it right you degenerates.

>>729028098
>.9999999....
white people
>1
niggers

>>729031466
Bertrand Russell (of Russell's teapot fame) disproved Set Theory over a century ago.

>>729031448
I said that already

>>729028098
It is.

Explanation:
Let's imagine what 9.9 really is. It's 10-1/10. What is 9.99? It's 10-1/100. So then what is 9.999repeating? It's 10-1/∞ or in other words 10-0, which equals 10.

So what you're all saying is that 1 - 0.999... = 0.
Therefore n - 0.999... = n.
Thus all numbers equal the two closest numbers <> themselves. And in an infinite progression, all numbers are equal to all other numbers. All because .999... = 1

>>729028098
Mathematically, yes. Effectively, no.

>>729031235
subtract what? 0.9999? 10-0.9999 is 9.0001 not 9? Also how can you subtract from 10x if there's still x?

>>729031812
>1/∞=0
multiply both sides by ∞ and get 1=0

Nope. 1/∞ is a tiny amount but not 0.

Literally arguing over 0.00001

>>729031834
OK let me make this a bit more logical
1 - .999... = 0
Therefore
1 + (1-.999...) = 1
and
1 - (1-.999...) = 1

Which means
n = n +/- (1-.999...) = n +/- 0
>+/- in this case means both plus AND minus.

Now turn that into an infinite progression and you get all numbers equaling all other numbers.

>>729032249
Not sure if retarded or trolling

>>729031630
This is not really a coherent mathematical statement, but for the benefit of others reading, I'll say that Russell made a great contribution to set theory by describing paradoxical sets that result from unrestricted comprehension.

>>729028455
no they are both exactly 1

check mathologer and he will explain it to you simply.

if you can't grasp it after watching his video then you never will and should not engage in discussions on the matter.

Doesn't matter what formulas you throw at it, .9999 repeating is not equal to 1. Because by definition .999 repeating is not 1, it is .999 repeating.

>>729032249
/b/ in a sentence

But actually, we're arguing over .000... the whole point of the ... is that there is no last digit.

>>729032010
effectively and mathematically yes.
draw circle
draw 3 lines from center dividing circle into 3 equal pieces. each piece is 33.3repeating%
erase 1 line
1 piece is 66.repeating % 1 piece is 33.3repeating %
remove last line and 99.9repeaing is left is the remaining circle somehow smaller?
no
99.9repeating% = 100%

>>729032571
But that also makes all numbers exactly all other numbers.

>>729032554
And all you've done by claiming 1=0.999... is constructed a similar nonsensical statement to that which Russell reveled in.

Congratulations. You've dug yourself into a corner that the genius Bertrand Russell constructed over a century ago.

>>729031834
> 1 - 0.999... = 0
correct

>Therefore n - 0.999... = n
incorrect

n - 0.999... = n - 1

>>729032706
The last digit is 1, it just comes after an infinite number of 0s.

>>729032762
Number LINE, not number circle. What you are saying is +infinity = -infinity because they occupy the same point on a circle.

>>729028983
eh?

flat earth = ignorant misunderstanding of blatant evidence and basic physics

.9r=1 = advanced math

how are these things related?

>>729028098
in reality 0.99999 isnt one but effectively it is

>>729028857
X= .99
10x= 9.9
10x-x=9.9-.99
9x=8.91
X=0.99

FTFY

>>729032903
0.9... is literally equal to one

google it faggot

>>729032840
kek

>>729032967
>FTFY
fuck off back to plebbit

>>729028098
1/3=0.33..
x3
3/3=0.99..=1

F(x)= 1/(x-1)

F(.999....) = -1,000,000,000...
F(1) = undefined

>>729032785
If they are not equal what is their difference? The real numbers (can be) defined as an equivalence class of limits of sequences of rational numbers. The elementwise difference between the sequence (1,1,1,1...) and (0, 0.9, 0.99, 0.999,...) converges to 0, so they are equivalent, so they are the same number.

>>729032775
oh shit your right! 2=46 wtf, serious, check it out.

>>729032785
It's not my fault you don't understand set theory and I'm not going to try and explain it to you. All you're doing is saying "Bertrand Russell" but not actually doing any math.

>>729033064
>Oh no, he's right, I should make fun of him.

Sir, you have injured me. I am mortally wounded. Ow! How will I recover? Woe!

of course it is you retard

>>729028269
>technically
The most autistic kind of -ically.

>>729033199
Nigga I ain't even the guy you responded to, now stop acting like an autist

>>729033154
This is a correct explanation, thank you for contributing

>>729033103
Are you claiming that -1,000,000,000... is a real number?

>>729028098
it is because the god said so

>>729033154
>converges
But are never equal.

>>729033168
I understand it better than you do, as you managed to make statements that were disproven over a century ago.

>>729033405
It is not real but it is defined

1/0 cannot be defined, even as infinity

>>729028098
At no matter what place you lead the 9s to, it will always be smaller, than 1.
And only get to equal 1 when you round up

>>729033365
The "sick burns" continue. I may be an autist, but you are truly special needs.

>>729033433
Real numbers are limits. Convergence is the same thing as equality

>>729032798
Whoops, meant to say
If 1 - .999... = 0
And n - 0 = n
then n - (1-.999...) = n - 0 = n
Thus, all numbers are equal to themselves minus (1-.999...) AND all numbers are ALSO equal to themselves PLUS (1-.999...) Thus, all numbers are equal to themselves AND their nearest decimal number <> themselves.

If this is true of all numbers, then all numbers are equal to all other numbers.

>>729033555
Up is down. Left is right.

>>729028098
It is. The most important part is the "...". Without it, then it is not.

>>729033490
What do you mean when you say defined? What type of number system are you working in? If we were working with the projective reals then 1/0 = infinity, no ifs ands or buts, so the question matters.

>>729033588
Nice math troll, saved

>>729033660
What do you think the real numbers are?

>>729032978
im going to explain to you why it in practice is but in reality isnt.

let's say you have to for some reason create a triangular building right. at the end of the day if you want the triangle to be equilateral the difference between 45 degrees and 45.01 degrees doesnt matter enough to be noticed so there for effictevly 45 and 45.01 are the same. but in actuality there is a numerical diffrence between 45, and 45.01. your number theory bullshit doesnt hold up in the real world. just because something can be effictevly the same doesnt mean it is. just because you can use olive oil instead of butter doesnt make butter olive oil.

>>729033745
I'm just trying to get a handle on this.
What exactly makes me wrong?

>>729033811
Numbers. Quantities. Amounts.

This is obvious to everyone but you who thinks they're sequences.

>>729033660
I hope someday to have as much time to dedicate to trolling as you seem to have

>>729033840

It presupposes that 0.9999... does not equal 1, and this suppostion is built into the logic. If it equals 1, then subtracting it from any number is the same as subtracting 1. The only way you get to the "nearest decimal number <> themselves" is if it does not equal one, at which point none of it matters since 1 isn't equal to 0.9999...

>>729028098
>I don't understand mathematics or modern physics: the thread.

>>729033840
"Nearest decimal number" isn't defined because the reals are so dense, you can always get a nearer one.

>>729033879
Ok, that's a useless definition. There are lots of numbers, quantities, and amounts that aren't real numbers. For example, is countable infinity a real number? It is an amount.

>>729033991
Just fun to mock retards in my spare time.

It isn't. The entire reason light travels so fast is because it has no mass.

Any object with mass can never reach the speed of light.

Even if it only had a mass 0.1-e99^99, it could never reach light speed. It could only get to 0.999999999... percent speed of light. That is not the speed of light, in that second you fell behind, light has pass you up by nearly 186 MILLION MILES.

>>729033836
It's not that they are effectively the same, it's that their difference is 0. We define decimals with 0 difference to be the same number, it's built into most ways of constructing the reals.

>>729033660
>look at me i have no idea what im talking about

Come back when you finish high school kid.

>>729034062
I kinda got that impression when I tried to write .000... and realized that's just an endless progression of zeros, which was not the same as I meant when writing (1-0.999...). Even though they are supposedly equivalent.

It's kinda like claiming a difference between nothing and no-thing.

>>729028098
Because it's not.

You can stretch that bitch into infinity but you will always need that 1

>>729031574

Riemann zeta function.

Also:

1+2+3+4+5... = -1/12

>>729034350
>can't defend his ideas
>must insult instead

Democrat detected.

>>729034426
I stretched your mom into infinity with my uncountably large cock last night

int (.9999999) = 1
float (.999999) = .999999

>>729034342
Ok, the way you'd say this rigorously is that the speed of anything with mass is in the interval [0, c). This is the set of all numbers between 0 and c, including 0 but excluding c. c is a limit point of this set, but it is not in the set. This set has no greatest element. There is no 0.99999... that is the fastest speed, because if there was I could just get the average of it and c, giving me a faster speed that is also less than c.

almost

In this thread, people who never got to calculus.

>>729034377
Welp, if it's worth anything to anybody, this argument convinced me that 0.999... really does equal 1. Largely because 1-0.999... = 0.000... which is just an endless series of zeros.
>color me impressed.

>>729034474
>mixing politics and math
we're getting into some advanced trolling techniques here, friends
what will we see next? race baiting? math cucks? reply to this post or the Riemann hypothesis is false? bananas?

>>729034694
You are on /b/

This is just a "loudest voice" thread.

If you want a real math thread you need to go to >>>/sci/

>>729034377
Proofs can be tricky. You have to make sure you're not assuming something that you don't mean to, it's easy to do on accident.

File: 1491750255145.jpg (95KB, 1471x1340px) Image search: [Google]

95KB, 1471x1340px

You fags

>>729028564
Wrong, this is how it's actually done.

x = 0.999
10x = 9.99
10x - x = 9.99 - 0.999 = 8.991
9x = 8.991
x = 0.999
/thread

You MUST respect the number of 9s, try it out with a calculator.

>>729034782
Please don't send these assholes to sci, you're going to ruin sci

>>729034484
Nice. Still doesn't prove me wrong.

File: Einstein's Hobby.jpg (73KB, 800x644px) Image search: [Google]

73KB, 800x644px

>>729034881
They'll get out-brained and sent home stupid crying.

>>729034890
I fucked your dad too

this is retarded lol

>>729034880
/thread

If anyone wants to actually learn this shit, look up real analysis. No-one will though, obviously.

>>729034987
found the 12 year old

>>729034772
?? You ok there? You started off with insults and now you seem to have totally lost it.

>>729028098
1/9 = 0.111 repeating
2/9 = 0.222 repeating
3/9 = 0.333 repeating
...
8/9 = 0.888 repeating
9/9 = ???

>>729035129
That one. That one is good. That one would convince a lot of people.

>>729028098
(1/3) = 0.33333333333333...
(1/3) * 3 = 1
1 = 0.999999999999...

retard OP, who the fuck taught you math, your gym teacher?

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>>729035088

File: fU3rMyNs_mmDQivvx-jypEFzz2KQIwrwgc09A5DrrMg.png (391KB, 638x480px) Image search: [Google]

391KB, 638x480px

For practical mathematical purposes, 9.9999 to infinity is 1, since it only takes a finite amount of infinity to reach a level we could measure anyway, but philosophically it isn't.

Big whoop faggots.

>>729028098
Depends on the topic? If someone is arguing semantics over .99999- not being one then they just need to be slapped. If it's something mathematical or requires precision then I agree.

>>729035129
this

>>729035299
99 dubs confirm, thread's over folks.

>>729035289
>"you're an idiot"
>"cuck"
>"troll!"
3 for 3 on terrible arguments. Just stick to the topic.

>>729028098
Objectively, .99999999~ is not 1. Practically, it may as well be 1, but only 1 is literally 1.

>>729033879
Actually, I'll also have to disagree with you here.
Real numbers are best treated an as infinite sequence of converging rationals, as outlined by Brauer. An easy way to represent this constructively is to treat any given real number as a function (or a formula), that for any given standard of "accuracy", returns the closest estimate of that real number possible.

>>729035299
It's not for "practical mathematical purposes", it is equal by definition. This isn't an approximation, it's a limit.

>>729035423
Wrong.

>>729035423
it IS one. ask ANY math professor

>>729035423
Wrong .9999 repeating is exactly the same as 1. Unless you are talking about the actual string of characters used to display the number, is which case you are a dumb cunt.

>>729028098
It is, you wrong.

>>729033199
x=0.999...
10x=9.999...
10x-x=9.999... - 0.999...
9x=9
x=1

>>729029350
U must be black. Gtfo nigger

>>729035436
Another way is Dedekind cuts, where you define them based on intervals of rationals that are unbounded below. Each such interval has a corresponding "upper limit", which is the smallest number bigger than everything in the interval. You can't find any rational between 0.99... and 1, so they have the same Dedekind cut, so they are the same number.

>>729035461
There is no limit for infinity.

1 - 0.000.........infinity.........1 = 9.999999999

>>729035385
Eat a log of shit out of my asshole

>>729028098
you guys don't know shit about math
>What am placeholders?
Name a number bigger than 0.999... but smaller than 1, GO

>>729029350
0.999... is definitly 1, and there are many mathematical demonstation of this.

It cannot be true.

Getting infinite dubs does not make your post number '1'

That post has already been written by moot in the prehistory.

>>729035693
.999... + .000...1

>>729030356
Define "never".

>>729035681
Limits to infinity are defined like this

lim x->infinity f(x) = L iff there exists an N for all E such that x > N -> |f(x) - L| < E.

this is why /b/ remains dead

stupid cunts doesn't read the catalogs


GO TO >>>/sci/


YOU FUCKING RETARDED KID

>>729035680
Nice, the words to define the numbers are obviously required to make judgement it seems. But it still depends on arbitrary limits, they are basically the same, but they stI'll aren't.

>>729032840
In an infinite serie, there's no "last digit".

>>729035775
What does that sum equal?

Suppose 0.999... < 1, then there's a whole number n such that 0.999... < 1 - 10^-n = 0.99...9 which is a contradiction. Therefore 0.999... = 1.

>>729033490
1/0 doesn't exist.
0/0 is indefinite.

>>729035555
QUADS GET

>>729035910
Whatever .999... means with a 1 following the final value of ... which can be assumed to be a '9'

Or

.999 ...91

Which is less than one

>>729035908
Define "in"

>>729035857
I think you should look up equivalence classes. They work like this. First we make up a way to catagorise things. Everything must have one and only one category. Now, we say that everything in that category is equivalent. Not that they are basically the same, equivalent. Obviously some of these are more useful than others, but the one that tells us that 0.9999 and 1 are the same is useful. It is the system we mean when we say "real numbers".

Another example is saying that all odd numbers are equivalent and all even numbers are equivalent. This gives us a logical system with even being false, odd being true, + acting like xor and x acting like and. In this system 1 = 3 because they both mean true.

>>729036018
Well 0.9999...91 isn't 0.9999 ... is it? There is no "last digit" on 0.999... and 0.91111... sure as fuck is smaller than 1 so what are you on about?

>>729035809
It literally doesn't matter, there is not one single calculation that requires infinity 0.999 to equal 1 or not. However, they are different numbers, as infinity 0.0~01 + 0.9999 = 1, even if practically they behave the same as 0 + 1.

They are not the same, even if practically they are.

>>729036077
"in" AKA "after"

>>729035555
He's got quads, so he's right!

>>729036077
If someone was to count to infinity, when would they stop? Never. Hence why the 9s never stop. Infinite numbers behave differently than finite numbers.

>>729036154
Sure there is. There is no value of infinite. So as soon as you are tired of writing 9s I'll swoop in and add a 1.

Fuck you.

>>729036077
An infinite series is a function that takes in a natural number and outputs something else (in this case a rational number). Something is in the sequence if there exists a natural number n such that f(n) = that thing.

Folks, look at it this way....
Think about the number 0.000....
It's an endless series of zeros.
There is no 1 at the end of it.
Because there is no end of it to put a 1.
And no matter how many zeros you add to the end, it's always going to equal zero.

So what they are saying is this. 1 - 0.999... = 0.000... which is the same as 1 - 0.
OK.
So if 1- 0.999... = 0 then .999... must equal 1

>>729036234
>There is no value of infinite
Ah, a retard

>>729036150
While I agree, who knows whether we will need to distinguish the two in the future. I don't see it personally but I don't see the future. The argument is literally a waste of words.

Until such a time they will be treated the same, until they need not be.

>>729035436
You: "A number is an infinite sequence of things"
Every non-retard: "A number is 1 thing."

>>729036168
Mathematically, that exactly what the = sign means.
It means both sides are equal, and therefore THE SAME.

If you can replace 0.9999999.... with 1, then 0.99999 is exactly the same as 1.
Not similar.
Not close.
Exactly the same.

And that has been show. 0.99999 repeating = 1, therefore 0.99999 repeating is exactly the same as 1, by definition, much the same way 1+1 is exactly the same as 2.

>>729036301
That's just a practical way of distinguishing them, rather than a philosophical one.

>>729034432
You're falling for a meme you cuck

>>729036168
Sure there is. For example, defining them as different numbers would break the topology on the reals. The metric topology would no longer be a topology (unless you were careful about adding these infinitesimals in, but by then you've created something completely different to the reals).

>>729035555
Quads of truth. 0.999999...= 1 confirmed

>>729036311
Ah someone who takes bait.

STEM faggots are easiest to trigger because they have the highest percentage of Autistic and Obsessive Compulsive people.

This mental instabilities disable them from exerting themselves when "someone is wrong."

Do you know what kiting is?

inb4 Damage Control

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I could be wrong but 0.999999... is an infinity which will always be getting closer and closer to 1 but never will. In an extremely strict sense, it is not 1.

>>729028098

0.99999.... is not 1.

if it was 1, it would say 1.

it says 0.99999....

it is 0.99999....

anymore brain busters?

>>729036481
Practical or philosophical, it still works. No matter how far out you take it, 0.000... will always equal 0.

>>729036474
Actually, we say that a number is an equivalence class of infinite sequences (or at least it's isomorphic to the set of them). An equivalence class is one thing.

Being careful with definitions is what lets us do fancy math. We need to know exactly what a number is before we can use them to their full potential. "A thing that tells you how much there is" just isn't good enough.

>>729036686

right. just like when you step forward half the distance with each step. you will never reach your destination because you are always less than the distance you need to travel.

Today is the day that I find out /b/tards don't know basic algebra.

>>729036479
Your clinging onto the practical and not the philosophical infinity.

While they certainly act the same when we reduce them to finite numbers, they are infinitly small in difference, which in practical purposes in a measurable world that cant deal with infinities is the same, but philosophically in a world that isn't bound by such perameters would not be.

>>729036708
Don't bring zero into this, that's a whole different thing. You're just trying to muddy the waters further.

>>729035129
if you have 9 pieces and you divide them in groups of 9, you wil have 1 group...
>having to explain basic maths
the same as 1/1 =1, 2/2 = 1, 3/3=1 ...

>>729036696
0.5 isn't 1/2. If it was 1/2, it would say 1/2.

Basically engineers will say 0.999...=1
because for any practical application, they're the same.

Philosophers or mathematicians will say 0.999...=/=1
because in an incredibly autistic and rigorous sense, they're not equal.

/thread

>>729031574
BTFO
T
F
O

>>729036826
No, they are exactly the same in the infinitely precise world of maths too.

>>729036584
Except it wouldn't. Creating a lie to bypass philosophical obstacles into practical terms is not above the mathematical community.

>>729035983
Neither 1/0 nor 0/0 exist. They are only abstractions of limits

>>729036943
No, mathematicians will not say that. Philosophers might, but they are wankers who need to pick a real field so who gives a shit.

>>729028098
1=1
0.99999...=0.99999...

1≠0.99999...
0.99999...≠1

Thanks for attention guys.

>>729036659
Dude, i just opened 4chan and i saw this retarded ass piece of shit post of yours.

Do you also tell others theyre cucks? Whats it like being a special snowflake? Are you proud of being math-illiterate? Youre american arent you?

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>>729028098
a/a = 1

1/9 = 0.1...
1/9 * 9 = 0.1... * 9
9/9 = 0.9...
1 = 0.9...

>>729036826
>>729036479
So respond to him on a practical level.

1-0.999... = 0.000...
Which is an endless series of zeros that never ends. You never get to put a 1 on the end because there is no end to put that 1. Thus, in every sense of the word, .000... EQUALS 0. No matter how many digits you take it out to, you will still have nothing but zeros.
and nothing but zeros is what???? ZERO.
Thus the difference between 1 and 0.999... is ZERO.

This even has an article in wikipedia. 0.9999...=1

>>729029852
Lol no you dumb nigger.

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>>729028637
x=0,999
10x=9,99

>>729036826
But mathematically, that difference is infinitely small, and therefore nonexistent. This is literally the definition of a limit.
MATHEMATICALLY, your philosophical infinity is irrelevant. And that's the point.

Mathematically, 0.999999.... is exactly the same as 1. Therefore, any cuck who claims they are different, wasn't awake for their math lessons.

Wanna argue philosophy? Tell me again about the number of elements reality is composed of - was it 4 (earth, water, air, fire) or 118 and counting?

Math: Proven correct, by definition.
Philosophy: Make believe that got it wrong about the real world since 4000BC.

>>729037008
Topology axiom 3: The infinite union of open sets is open.

U_{n = 1}^{\infty} (1 - 1/n, 1) = {0.999...}.

Now either: 0.9999... is open, which would be weird and awkward since it is a singleton, or one of those sets I'm unioning isn't open, which is weird because they are intervals that don't contain their limits.

>>729037271
Wikipedia. Famously reliable wikipedia.

>>729028637
10(.999) = 9.999
9.99 =/= 9.999

>retarded

>>729037389
Fucked that up, my bad. Like 4AM here, but you could do a very similar construction without fucking up that bad and get a similar result.

>>729028510
this

>>729037389
Apprec8 the effort lad, at least someone here isn't an innumerate mong.

>>729037379
>infinitely small, and therefore nonexistent
yet infinitely small != nonexistent
mathematically

99 is not 100

>>729037456
It boils down to "(0, 1) now has a largest element, which is weird and makes the concept of it's limit points vague and poorly defined"

>>729036686
Yes you are wrong

>>729037568
Can't get any smaller than non existent, dude.
At least, I've never heard of a negative size
>your penis is the exception that proves the rule.

>>729037533
>innumerate
Innumer8

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>>729028098
0.99999.... is 0.99999....
1 is 1
op is faggot
BBC > whitey cuck baby cock

>>729028098
0.999 tends to one. It will never reach one in mathematics. However in Physics you have a certain amount of +/- error so it will.

x = 0.9999....
10 x = 9.99999.....
9 x = 9
x = 1

fuck you 0.999999 = 1

>>729028098
>is NOT = 1
is not is 1
!= =1

Are you a nigger?

>>729037594
One thing I can say it definitely will break is the Hausdorffness of the reals, which is a super nice property.

You can get it back by making {0.9999} and {1} open, but you have

\cap_{n = 1}^{\infty} [0,1] = {0.999..., 1}

Therefore {0.(9), 1} is closed. Both of them are open, therefore it's clopen. Therefore the reals are no longer connected.

So you have to choose from either Hausdorfness or connectedness. And you want both of them. That's basically the argument I was trying to make the first time before I rushed it.

>>729037568
Prove it, cuck.

Let us say 0.000000...... repeating....1 is infinitely small but not nonexistent (that is to say, =/= zero).
This means there must exist a number n, where 0 < n < 0.000000.... repeating....1

It is my claim no number n that fulfills that condition exists.
Want to prove me wrong? Write the number n.

>>729038064
\cap_{n = 1}^{\infty} [1 - 1/n, 1]*

>>729028098
0.999999....=1
But it's just because the human brain cannot comprehend the term infinity.

>>729028269
Technically this is your opinion and in my opinion not true

>>729038304
As you wrote it, you are right.
But 0.000...repeating...1
is NOT
0.000...
The latter repeats zeros infinitely. What you wrote has a definite end. The two are not the same.

>>729038477
Honestly, infinity is super well understood.

>>729038594
Is 0.0000... equal to 0.000....0?

>>729038595
Not judging by this thread.

>>729038719
I mean by people who actually know what the fuck they're talking about.

>>729038649
0.000... has no end. Therefore, there is no end to place a 1. No matter how many digits you extend it, it's still just a whole lot of zeros.
And no matter how many zeros you have, they all add up to zero.

>>729038649
What is the last digit of Pi?

>>729028407
constructs are constructed
get angrier

>>729039024
>>729039084

Yeah I know, I was point out that "They are not equal because on has a last element" is bullshit, because those two are definitely equal but one has a "last element". Socratic questioning guys.

ITT: Anon tries to math.

If you guys care so much, go to school and take math. Or look up what a limit is.

>>729028098
YES IT IS

>>729039400
what limit is
>a construct

>>729039555
what math is
>a construct

Calling something in math a construct is like calling something in science a theory. Makes you sound smart to people who don't know how those fields work.

This problem shows that maths is as subjective as any other subject studied by man (not a pure science). 1=0.9(999) only if you assume that any use of infinite is acceptable to answer a question in a quantum universe, you think rounding errors are acceptable and not an arbitrary rule or you think for some reason any derivation from "Real" 1 can still be "Real"1 and not a separate number requiring a different label.

>>729040192
It is not subjective. Mathematics is the study of definitions and their implications. I could completely, unambiguously define the set of real numbers based on set theory if I wanted to, there is no subjectivity in it.

In fact, for something to be a set it has to be defined unambiguously (be well defined).

Obviously which definitions you take is subjective, but that's like saying biology is subjective because you can choose which creatures to study.

>>729028098

Multiply by 10

9.99999 ...

Subtract 9

0.999999 ...

You get back the same number, so

so 10x - 9 = x

solve for x

10x - 9 = x
9x = 9
x = 1

Oh shit, you're retarded OP.

>>729040516
constructs for all my self-proclaimeds

>>729040481
Are you saying there are multiple fields of maths that are all true if there rules are followed? Hence the answer to this question is both answers are true?

>>729032040
theres never a 1 at the end of 1 - 0.999....

Theres never a last digit.

>>729032051
infinity is not a number, it's a concept

1/x as x->∞ is 0. you can't "divide" by ∞ since it's not a number

>>729032651
Synonyms can't mean the same thing because they are different words!

>>729035775
.000....1 makes no sense, there is no end to the zeros. There can never be a last zero

>>729036686
>1 is infinity

you are retarded

>>729037379
>the difference is infinitely small

wrong, there is no difference

>>729040649
These are not fancy tricks. They are using the fact that the real numbers are a field. If this didn't work, then the reals wouldn't be a field. And that would be bad, m'kay? m'kay.

>>729034432
Riemann zeta function is an complex number function and I don't see how it applies. The natural number sum ( 1+2+3...) is a valid sum and was discovered by Euler.
BTW, just for discussion, 1+2+3+4+5... is an example of why Bosonic String Theory is in 26 dimensions. The number of string theory dimensions is the reciprocal of 1/2 the Euler natural number sum + 2. Now we are into advanced math.

>>729040725
All truths are conditional. If we are talking about the real numbers, then the answer is unambiguously yes, they are equal. If we are talking about a wacky new number system OP has come up with, the answer could be yes or no. But the assumption is that we are talking about the reals, because they are used so much more than everything else that assuming anything else would be like assuming that a human isn't from the Earth because they haven't specifically told you they are.

>>729040779
they aren't fancy tricks
they are constructs

does not equal 1 but is infinitesimally close to it

>>729035788
What a fucking faggot statement. Point is, the more recurring decimals the closer it is to 1, but for any defined number of recurring decimals the number does not equal 1. Meaning that whilst the number of decimal places is a natural, positive integer the recurring decimal cannot =1.

>>729040747
To be fair, there are number systems where infinity is a number, like the extended reals or the projective reals.

>>729028857
you are a fucking idiot

>>729040969
Sure, math is composed entirely of constructs. My point is is that these constructs come from us wanting the real numbers to be a field. Them being a field is good, it lets as do cool stuff.

>>729041196
No they are not numbers in those sets, just elements of the set

>>729028098
1/3 * 3 = 1/1 = 1

1/3 = 0,3333333333333333
*3 = 0,999999999999999
=1/1
=1

>>729041125
But the number of decimal places is aleph null, which isn't a natural, positive integer. So that point seems pretty shit.

>>729041424
1/3 =/=0.33333333333333333333333333 it =1/3 and cannot be converted

>>729041406
If you can't call elements of a number system numbers then idk what the fuck number means.

Jesus fucking Christ
/b/ 's avg math skill is just horrendous

>>729028098
Depends purely on the situation. 0.999... is not 1 if it's an asymptote for example.

>>729028753
this guy calls people dumbfucks but can't even read a complete line like a dumbfuck

>>729041570
Sure, and if it's a pig it also isn't equal to 1. An asymptote is a curve. 0.99... isn't a curve and I don't know what it would mean for it to be an asymptote.

>>729041714
With an asymtote in 1 you can reach 0.999... but never 1. Therefore 1 is not equal to 0.999... in that case.

>>729041521
take an integer number, for example 1000 trees.
If you want one third of the trees, you calculate 1/3*1000 which equals 333 trees.
so 0.33333333333*1000=333.3333333333333.
But since its an integer number you have to cut the number after the point.
This equals to every integer of every value
so 1/3 = 0,33333333333333

>>729041937
>>729041714
Oh no nevermind. https://math.stackexchange.com/questions/921014/is-0-9-repeating-1-disproved-by-asymptotes disproves my idea.

>>729041937
Right, so you're saying that the sequence {0, 0.9, 0.99, 0.999} asymptotically approaches 1, so therefore 0.99.... isn't equal to 1. That doesn't follow. In fact, the exact opposite follows. Having a decimal expansion approach something asymptotically is what we mean when we say "equals".

>>729042129

Props for looking stuff up and actually accepting arguments.

>>729029852
>Using infinite and don't understand it.
Infinite dumb.

>>729030814
It's literally equal.

>>729041521
He means .3333... obviously you pedantic nigger

>>729028098
Correct. If 1 were a straight line, .999... would have the slightest curve and therefore would never be parallel.

>>729043401
No they wouldn't, because as has been proven at least a 1000 times in this thread already, 0.9999... = 1.

So you wouldn't even have two lines, they'd be the SAME line.

>>729043547
constructs constructed by and for the construct

.33333(...) = 1/3

multiply both sides by 3

>>729043680
Given how math is nothing more than sets of internally consistent man-made constructs, your counter-argument is literally meaningless.
"Mathematical construct 0.999999... != 1"
"According to this valid mathematical construct you are dead wrong."
"Only if you're looking at constructs!"

>>729028098
it isn't but mathematicians decided to go full retard so it is according to their definitions

>>729028098
So... Of what I've gathered from this thread 0.999... IS equal to 1. Because it is infinitely close to 1. Keyword "infinite"

Then 0.111...=0 ?

I'm an absolute retard in math so... Yeah, sorry for asking dumb shit.

>>729044615
No. You can only write numbers that terminate and aren't 0 this way. So 0.5 = 0.4999999 and -2.3 = -2.2999999.

>>729044615
no
0<0,1<0,111111<0,12 so its obviusly not zero

>>729028098
x=0.999999999...

10x=9.9999999999.....

10x-x = 9.999999999.... - 0.99999999....
9x=9
x=1

but x=0.99999999......

So

x=1=0.999999999....

1=0.99999999....

there was time when math didn't like infinity and everything was perfectly logical
and then retards came, accepted infinity and other stupid shit and now half of math is pretty much disgusting
all the old, classy mathematicians must be turning over in their graves

Something something Taylor series proof something something.

It is.

>>729044801
Oh yeah, you're right. So in order to have a number infinity close to 0 it would have to be a 1 at the end of 0.000... But obviously is impossible cuz it has no ending.

Whoah, today I've learned something thanks to /b/

>>729045399
>But obviously is impossible
you can make something like this: 0,(0)1

>>729044972
Those days were called preschool, I miss them too tbh

>>729045670
preschool at least sticked to logic

>>729045615
Challenge: Write out the sequence that represents. For example, 0.(34) represents {0, 0.3, 0.34, 0.343, 0.3434, ...}.

Protip: It's just 0s.

>>729044972
To make it more confusing, in the late 1800's, Cantor discover trans-finite mathematics where the are numbers beyond infinity. In fact, there is an infinity of infinite numbers, each one larger than the previous.

>>729045615
How do you call that abomination?

>>729033836
Math has absolutely nothing to do with the real world, nor does it claim to that is the entire point.

>>729038507
Learn math, then we'll talk.

>>729045772
Everything in math is perfectly logical. For example, the limit as x approaches infinity is defined as (copying from a post from earlier)

lim x->infinity f(x) = L iff there exists an N for all E such that x > N -> |f(x) - L| < E.

This is perfectly logical and doesn't involve any vagueness.

>>729046113
absolutely nothing that involves infinity is logical

>>729028510
Easiest answer. There is a more difficult one, too. Check, let's say, Wikipedia or math textbook.

>>729045988
Cantor was an idiot

Colombian scientistic here
0.9 IT IS NOT 1
Nor 0.999 0.9999 0.99999
0.9... (PERIODIC) it is 1.

Done.

>>729046292
Why

>>729035299
> a finite amount of infinity
fucking nice

>>729046203
I just gave you a counter example. For example I'll claim that lim_{x -> \infty} 1/x = 0. Fix an E > 0. Since the rationals are dense it is possible to pick one less than E. The Archimedean property guarantees I can pick an N such that 1/N < that rational. So if x > N we have 1/x < 1/N < E.

In short, the function gets arbitrarily close to 0, so the limit as x approaches infinity is 0.

>>729046385
because he created a theory based on his own ideas only and later even denied by by himself
oh, and he went full misticism