>>>/sci/9736828

Brainlet asks if any mathematical concepts rely on the identity 0.999... = 1, which he considers to be flawed. Multiple anons prove him wrong, he cites IEEE floating point standards as "proof" that infinity is inconsistent, and posts multiple bullshit proofs, says he's a "programmer"
160 replies later and i'm here

>make some false or divisive statement
>????
>profit

OP got baited too hard now he's posting on other boards for reinforcement

it's every day, i can't take it anymore user

>The monkeys have been caught and put back in their cage
Sorry for the inconvenience buddy

>he thinks the picture implies a question
>he doesn't know that 1? is a valid irrational number

N = 0.999...
10*N = 9.999...
10*N = 9 + 0.999...
10*N = 9 + N
9*N = 9
N = 1

i don't see any problem, it's just basic math

Retard implying infinity is a number because IEEE754 uses a special number for representing infinity.

No need to make it so complicated. Literally just:
1/3 = 0.333...
2/3 = 0.666...
3/3 = 0.999...
1 = 0.999...

K Jow Forums, since the undergrad brainlets at /sci/ can't refute simple questions in mathematical form, let me enlighten you. But to be clear, I don't agree with the troll/idiot in that thread, but the confusion usually doesn't come from understanding infinity, but the weird equality sign.

0.999=1 makes no sense. It's nonsense because 0.99999 is not really a correct representation of 1. What does it mean? It comes from the notion of convergence. Convergence is just the idea that a collection of of numbers can get arbitrarily close to some value. What you can prove is that if you keep taking 0.9999999s with enough nines you can make the distance between 1 and those numbers arbitrarily close to 0, this is trivial here as if you take some number 0.0000...01 with k number of 0s (this is finite so no problem with notation) and you want to approximate it such that the error is less than that nuber you just take 0.999s with k+2 number of nines you see that 1 minus that number is our error. So we say that collection of numbers converges to 1, but there is no formal notion of adding infinite times. What happens, however is that when one is constructing the real numbers from the ground up a standard approach is using the rationals numbers, that can be defined with no problems from the integers which can be defined with no problem from the natural numbers. However, it important to note that how it's constructed you usually collapse into a single element elements that are equivalent to each other. For example, you identify that 2/3=4/3, but the rational number is considered formally as all such fraction, but to not use preconceived ideas you say two rationals numbers a/b , c/d are equivalent if a*d=b*c, using the product defined on the integers (which are themselves identified similarly using the natural numbers). For the reals, you talk about cauchy sequences which look like they converge, but not where it converges, you take a notion of equivalent sequences to define the number.

9 * 0.9 = 8.1
9 * 0.99 = 8.91
9 * 0.999... = 8.999...1

>dun goofed

To expand a bit, a sequence is just a collection of objects that are ordered by the natural numbers. This is formally defined as again the naturals can be defined with set theory, but you are talking of a set with distinct objects. For example, the OP has the sequence {9/10,9/100,999/1000,..} And here the dots make sense because it's not an infinite sum, but rather, and infinite number of distinct rationals. Now you take from the rationals all sequence that are cauchy, this is just that you for every positive number (arbitrarily close to 0) you can find a place in your ordered sequence such that all the numbers that are past that index, their difference is less than that number. You take that two sequences are equivalent if you compute the sequence where you take the the difference by taking the difference point wise, and they are equivalent if that sequence converges to 0. Now, 1 and the other sequence are identified like that, but this doesn't mean there is a strict equality, but they are all elements of the equivalent class of 1.

This may sound pedantic, considering are much more simple arguments, but the idea of infinity in math is taken with care to avoid various paradoxes.

yeah it only works when you define the .999... to be an infinite series, which is to my understanding is the standard definition.
That's why i usually use 0.\bar{9} in latex

Eh, not really. Infinite sequences can be defined in a sequence space en.wikipedia.org/wiki/Sequence_space but the problem arises with what exactly 0.999... which is more complicated because what you have is actually an infinite collection of rational numbers that converge to 1. There is a bijection from the reals to the the space of all sequences that only contain natural numbers (this has a bit to do with cantors famous argument), but that is an identification, which is a bit problematic in decimal notation as this example shows you can identify the same number with two different objects. What can be donde is to collect all these identifications and put them into a whole package called an equivalence class. The equivalence class is a generalization of the concept of equality, so the notation can be justified, but it is still not really all that clear.

What the fuck 0.999... even means?

Cauchy created mathematical analysis almost 200 years ago so we didn't had to deal with poorly defined infinitesimal bullshit anymore.

Yet you idiots keep screaming about a problem that is only a problem because you don't have jackshit idea of what you are talking about.

0.999... = 1 - epsilon

>so we didn't had to deal with poorly defined infinitesimal bullshit anymore

As a physicist, i deal with plenty of bullshit infintesimals on a daily basis, regardless of cauchys' contributions to analysis.

As a non meme physicists, that's just compact notation to avoid cumbersome formalism when dealing with applied results. That doesn't mean you are not expected to learn analysis and higher level topics as they have become fundamental in modern physics.

At work we use "unlimited" a lot for code paths often taken by clients with deep pockets. It isn't maths though, it is logic.

Are you retarded? Infitesimals show up plenty in theory as well. Heard of a delta potential?

Delta potential isn't even related to infinitesimals you retard, the problem with the delta function is treating it as a real valued function that has the property of vanishing at all points and except one which is "infinity". The intuitive notion should be to consider an event that has a spike that's large enough to be considered infinite an localized, and in PDF theory as a sort of generlized kronecker delta useful in QM. But the formal definition has to go beyond normal finite dimensional analysis.

>The monkeys have been caught and put back in their cage
Oopsie woopsie! We made a fucky wucky!

Dudebro, read it up on wikipedia to understand it:

>en.wikipedia.org/wiki/0.999...

1 and 0.999.. are really two differnt representations of the same number.
In fact, you can do this for every whole number:

1.9999.. = 2
14.999.. = 15
99.999... = 100

It's confusing, but you have to realize that in our number system the same numbers can get represented by different symbols, ie. 1/2 = 2/4 = 0.5.

This is not differnt.

>LOL
t. brainlet

I'm sorry

ITT: People who can't understand the concept of infinity.

t. freshman

infinity doesn't exist in computer hardware

No, there's no such thing as 0.999 anyway computer scientists only care about natural numbers. Real numbers are for fags and any problem involving real numbers isn't even a problem if you have an infinite amount of numbers between adjacent integers.

0.9(repeating forever) is not equal to 1.

While I'm at it, 0.3(repeating forever) is not equal to one-third.

Dumb twits don't realize that there are concepts that simply cannot be expressed accurately in certain systems. The reason why when things like one-third or two-thirds are written numerically they repeat forever is because no matter what you do, no matter how far you take it, you will never reach the exact value of that concept when you write it in that format. It is merely the closest value that can be expressed in that format, not the true value.

>IEEE floating point standards as "proof" that infinity is inconsistent
is /sci/ just full of undergrads who think they're smarter than they are?

just imagine a burrito.

Best troll I’ve seen in a while, almost got me

A Monad is simply a category on the endofunctors of mogoloids, what's the big deal?

xD upvoted!

0.999... = 1
0.999... = 0.99...8
0.99...8 = 1

Is this True?

There's no ...8. There's no ... followed by anything.

Please don’t pull /sci/ shit into Jow Forums. We don’t need trash from that board polluting the trash on this board.

0.999...99 = 1 - 0.000...01

Kind of. Just be aware you’re working with limits and not numbers
Physicist do that all the time when multiplying infinitesimals by each other

1/3 = .333...
2/3 = .666....
1/3 + 2/3 = .999...
1/3 + 2/3 = 3/3 -> 1

Attached: 18527877_10155356404617451_5296671420433799465_n.jpg (540x397, 45K)

Floating point infinity is actually infinity. It obeys all the rules of infinity, in a normal extension of the real/complex numbers. The concept of infinity can be modelled, but in practice there aren't things that reflect the concept of 'infinity' in nature, sure.

>0.999... = 0.99...8
Wrong.

Take an axiomatic construction of the numbers. The idea is how you interpret "equality". It's more tedious and less trivial, but an expression such as 1.9999 is not constructible from the rational numbers. It's not "wrong" in a non pedantic way, but how you define representation of a number is wierd and what you are actually talking about is convergence of an infinite set of finite sums. Infinite sums are not defined as an infinite number of algebraic sums. That's called the generality of algebra, which has been left behind for the paradoxes it give. For example you can have a convergent infinite sum, that if you rearrange the terms (commute the sums) you can get a divergent sum and also you can make it converge to every number you want. en.wikipedia.org/wiki/Riemann_series_theorem
Yes, I saw this shit as a freshman, so it should be basic for any mathematician.

>especially cause functional programmers have no interest in explaining...
Especially because functional programming is a dumb meme that provides no benefit.
>make kode without using variables or mutable states
>make kode without using iteration
>presumably this means that nothing can go wrong because nothing is really changing
>compile it into machine instructions that actually are iterations and actually use variables
And as if that wasn't enough:
>do everything recursively
>the compiler works it out as an iteration because it realizes it's more efficient
Fucking idiocy. You can't imagine the amount of time I've spent talking to functional programmers; they can never answer anything because they are the first ones to not understand FP. All functional programmers are monkeys.

1/3 + 2/3 != .999...

but does .333... + .666... = .999... ?
i know there are other ways to prove this but this is what i came up with, haven't seen it used ever

You can't model infinity in a math equation. It doesn't follow the normal algebra rules and its meaning can vary depending on context.

That's not what he said though. 0.333...+ 0.333... + 0.333... = 1. It's because 0.333... is 1/3.

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1/3 is not equal to 0.33...
1/3 is not equal to 0.33...
1/3 is not equal to 0.33...
1/3 is not equal to ...

then nigger what is it equal to
i dropped out of high school at 16

That perfectly describes /sci/.

3^-1

i see. have a nice day.

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wtf so theres no number before 1.0?

Imagine being such a mathlet brainlet and getting so goddamm booty blasted that you have to run off to another board to try to get in insults and quips behind your opponent's back.

Math majors are cowards.

>0.3... != 1/3

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1/3 != 0.3
1/3 != 0.33
1/3 != 0.333
1/3 != 0.3333
1/3 != 0.33333
1/3 != 0.333333
1/3 != 0.3333333
1/3 != 0.33333333
1/3 != 0.333333333
1/3 != 0.3333333333
you can do this forever.

What if i have to take a shit.

Do I get vacation.

Do it in base4

Even 1 = 2, if margin of error, let's say, is equal to 3.
There will always be some margin.

Does

.777...

Equal

.8

?

Attached: .999...cequals 1.jpg (953x613, 113K)

Only if it repeats.

1 / 3 = .333333 (repeating forever -- inf limit)
.33333 (repeating) * 3 = 1

thats what i've been trying to say but is being pedantic

No.

While you're right about the confusion probably coming from the equals sign, proper notation for this does exist, it's called a limit

1/3 = 0.1111...
2/3=0.2222...
3/3=0.3333...
1=0.3333....

yes, but the limit is taken as well, 1. What you have here is a set containing {9/10, 99/100, 999/1000..} which is composed of finite representations of rational numbers and then you say the limit of this is 1, but there is no object in your set that is .99999999... non terminating. That notation must be introduced in sequence space. In here the notation is that this particular cauchy sequence is equivalent to 1, so you can justify limn-->inf x_n =1 but the crux here is that you are not actually talking about something called 0.9999, but you can interpret that as a sum, whose infinity symbol, doesn't correspond to the notion of adding infinite times, but with convergence. It's more about the algebraic "proofs" which use en.wikipedia.org/wiki/Generality_of_algebra which has no longer any meaning in modern mathematics. And while you say that at the end the notation can mean the limit, 0.9999... is not a valid representation of real number as constructed from the rationals, because the real numbers are constructed as equivalence relationships that are defined in notions of convergence. So yea, you have multiple representation, but the number itself is the equivalence class of that number. I argue, that you can say that equal sign is notation for the equivalence relationship, but you cannot use addition on them, because both are just elements of the rational numbers, and infinite sums are not defined.

The eternal /sci/ bait.

I wrote my disseration on this topic and failed the class.

>0.999... = 0.99...8
proof:
0.999... = 1
-1 -1
-0.000...1 = 0
*-1 *-1
0.000...1 = 0
0.999... - 0.000...1 = 0.999... - 0

Ah I see, sorry, that's a funny way to think about 0.999... I hadn't considered what equivalence really means in this way
Real numbers truly do break things that were once simple, if flawed

Where did you learn how to do math lmfao

If 0.999... = 1
0.98999... = 0.99
0.998999... = 0.999
0.9998999... = 0.9999
0.999...89... = 0.999...
0.999...89... = 1
For any n < 1, n=1

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If you, naked, was in a room 1 meter away from a 9.999999.../10 chick, and every 10 seconds you moved so that you're exactly half the distance you were prior (1 meter, 0.5 meter, 0.25 meter, etc.) then according to you, you'll never get to fuck that chick, but for everyone else on this board, you're fucking after 10 turns.

That's the 0.9999999.. .= 1 argument.

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No, after 10 turns you would be 1/(2^10) meter away. Nice meme though. But it has nothing to do with argument, it has to do with how decimal notation is defined and how the construction is done, in the sense that you are fundamentally talking about different equalities and there is no such thing as a 0.999.... But rather a sequence that converges to 1.

>No, after 10 turns you would be 1/(2^10) meter away. Nice meme though. But it has nothing to do with argument, it has to do with how decimal notation is defined and how the construction is done, in the sense that you are fundamentally talking about different equalities and there is no such thing as a 0.999.... But rather a sequence that converges to 1.

>sees 0.999... converges to 1
>can't see that 1/2 ^ inf converges to 0

you rite.

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Guess it's because most programmers don't even use seires in their code and think double is good enough.
Well, I don't care about this since passing numerical methods classes either.

You said after 10 turns you retarded faggot.

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>What did he mean by this?
Approximate calculations involve proofs which operate with infinity (infinite sums) to prove that you can achieve any precision of calculation with breaking down in enough steps.

Other than that: yep, there is no infinity in computers. However, the point he makes is void because he chooses to absolutely ignore infinite sums theory.

Do you even infinity?

It's 1/3 undergrads about to drop-out, 1/3 LARPing highschoolers and /lit/ pseuds (identical) and 1/3 schizos. There are few exceptions, like the animu faggot physics grad - he knows what's up. Overally, it's a bunch of monkeys googling big words and masturbating over online IQ tests (/sci/ version of consumer wars on Jow Forums).
All in all a great place to be.

so the exceptions are 1-0.999...?

Not him but I see what you did there and yes, it's stunningly accurate

>m-muh wolfram

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Not an arguement

Unfortunately that's correct, the exceptions don't hang around anymore.