0.999~ ≠ 1

So you really don't understand math, do you? You apparently don't understand what circular reasoning is.

So think of 0.999... as a distance and 1 as the destination. No matter what you do, you can never reach that destination. Saying 0.999... = 1 means you cheated and reached out to smack your destination because its utterly right there forever. That doesn't mean you actually reached it if you stuck to the original distance.

Think another way, it is literally the exact opposite of the speed of light in that you are virtually frozen in place...moving but never reaching.

What the fuck are you blathering about? Your metaphor is both terrible and wrong.

Or just beyond your comprehension

PS: It is.

Aww shit

All math since Newton BTFO

How will limitfucks ever recover?

No, it's just bad. 0.999... is just a notational variant of 1. Both are completely equal. This can both be shown arithmetically.

...

Approaches 1 is good enough for me.
My emphasis is combinatorics and related shit though, couldn't care less

So what's 1 - 0.999... ?

obviously 0.000...

Ok so I have a question. 0.333... equals 0.34, right? And 0.34 * 3 is 1.02. How is this possible?

That's what I thought. That would make them equal I guess

>0.333... equals 0.34, right?
No it doesn't. That is an approximation.

>Zeno's paradox.
Oh wow.

>mathematically impossible
There is no contradiction in 0.999... = 1 but there is in 0.999... + 0.000...1 = 1 for the Real set

Try to actually put some effort into learning real maths and stop being a fucking disgusting sensing-type brainlet

also for two different real numbers to not be equal, there must exist another real number in between those two numbers, but since numbers of the form 0.000...n do not exist in the real number set, there are no real numbers greater than 0.999... AND less than 1

There are. [math]\rm 0.aaa..._{11}[/math] is greater than [math]0.999..._{10}[/math].

they are actually equal

Ok, so if it's a distance and 1's the destination, what's the error from your distance to destination?

ie

|0.9999....-1|=?

"glitches" are real. If our current axioms and definitions imply that 0.999...=1 (which they do), then it is what it is.

If you prefer a different set of axioms and definitions where 0.999... =\= 1 then I would be curious to know what they are.

0.000...1 is nonsensical. It implies an infinite chain of zeroes but it has an end? Thats a contradiction. Thiw number cannot exist

let me explain to all the brainlet why 0.999 =/= 1
1/3 =/= 0.333
why? because you cannot divide 10 by 3 therefore even if you have indefinite amount of 3 following it will not be equal to 1/3. You cannot express 1/3 in base 10.

You are a mongoloid. Good to see mathematical illiteracy is still widespread today.

First of all, 0.999... is a rational number since it only consist of a repeating decimal. Thus, it must have a quotient to represent it. Since it can't be directly represented by a quotien, it must be equal to something that can be represented as a quotient.

It can be represented as the infinite sum below.
>9*(1/10)+9*(1/10)^2+9*(1/10)^3...¨
This is the geometric series seen below with a=9 and r=1/10.
>ar+ar^2+ar^3+ar^4+ar^5...
The solution to this geometric series is seen below, when the summation is done to infinity and |r|ar/(1-r)
We insert the given numbers for the representation of 0.999... and get that it is equal to one.
>(9*(1/10))/(1-(1/10))=(9/10)/(9/10)=1
Even though limits have been used, it can be argued that 0.999...=1 because it has to be equal to something that can be represented as a quotient, because it is by definition a rational number and can't be represented as a quotient in and of itself.

then how can you have an infinite string of 9's?

In ordinal arithmetic there is the concept of "infinity plus one".

why can't we imagine infinitely many 0's followed by a 1?

Because this implies that the series is not infinite, since it has an end after which you place a 1. It makes no sense to talk about an infinite series of 9's with a 1 at the end, since there is precisely no end to the series. A concept like 'infinity plus one' may make sense when for example you are speaking of the cardinality of a set, but it makes none in this context.

OP is right. Also, the set of all rationals is greater than the set of all integers.

>kid who says infinity is a number

Infinity can be treated as a value. In fact, some infinities are greater than other, for instance [math] \aleph_0 < \aleph_1[/math]. It baffles my mind that you would discuss the concept of infinity on a message board dedicated to math and science when you don't even seem to know what is taught in a first year math course.

>the set of all rationals is greater than the set of all integers
Sometimes b8 is far too obvious.

And of course, there are only finitely many primes.

"0.9.. /= 1"ers: Learn about equivalence classes of limits of rational series or about Dedekind cuts. If this is too hard, you might enjoy:
youtube.com/watch?v=PvceKeHl0Sg

easy proof:
suppose .99999... and 1 are distinct real numbers
now b/c real numbers are dense you should be able to find some x s.t. .999999... < x < 1
no such x exists
.99999... and 1 are not distinct
they are equal

what about 0.999.................10

Previous comments have addressed this already.
Note that I've advised your caretaker that you are on the internet without supervision again.

>ye bruh i bright infinity is number
>mathematical illiteracy
it's like you are saying infinity is a natural or real number, which it is not
0.33... is only but an approximation of 1/3

No. Go back to school.

Finally! SOMEONE who knows what they're talking about!

Suppose you tell me that .9999 is not equal to 1 because it is different by .0001. I will agree, and say that the number actually has another 9, and so is .99999. Then you will say "Aha! It's still off by .00001!"

It is clear that this process will continue forever.

I think there are arguments for either side:
---You could say that no matter how many 9s I add it will never be 1. This is true.
---I could say that the difference between .999... and 1 can not be a number greater than 0. This would also be true.

I think it comes down to physical interpretation, which is why mathematics was created in the first place. From a physical standpoint, there's no denying that .999....is equal to 1 in every sense of the word equal (and if you have some threshold for how close two numbers must be for you to allow them the adjective "basically equal," that threshold will surely be surpassed).

Have you stopped to think that the problem isn't that the original statement is wrong, but that the math used to prove it is wrong is flawed because we don't yet fully understand math? Hence our current understanding tells us something that is in reality impossible?

>the math used to prove it is wrong
Math as such is not something that can be wrong, at least not in the sense you are implying. You can make mathematical errors, but there is no true math as opposed to false math. Mathematics is simply finding conclusions that necessarily follow from a set of axioms. Whichever axioms you choose is entirely up to you. From the axioms we traditionally accept, [math] 0.999... = 1[/math]. You could develop a mathematical system in which this is not the case.

I question that. You may be perfectly correct, but you also may not be. I feel like we are still stuck in the dark ages of our understanding and that math is not as universal as we like to assume.

I feel like we are still stuck in the dark ages of our understanding

what makes you think that?

This simple equation and the fact that people think it is wrong because of our current evolution of math that can claim otherwise...

>0.999... ≠ 1

let x = .999...
therefore 10x = 9.999...
10x - x = 9.999... - .999...
9x=9
x=1
therefore .999...=1

where did i make a mistake?

that's what I'm saying

The real question is

[math] 0.000... = 0 [/math]

ITT OP is a brainlet and can't accept a fact with countless proofs

saved you guys some time

>An open set is the same thing as a closed set!

>computers using floating points to approximate decimals: .999~ = 1
>EEs modelling electrical wave forms in real life: pi = 1
>Astrophysicist measuring the energy of a blackhole jet: 100=1

heh, I laugh at your analysis and pure math.
(as a math grad I understand your pain but do not share it cuz physics>math imo)

If .999 = 1 why don't they just write 1?

check and mate

The problem is that the so called "Reals" aren't real, which means any arithmetic or math done with them is pointless and retarded.

[math] 0.333...[/math] and [math]\frac{1}{3}[/math] are not sets dummy.

Assume 0.9999... != 1
OP is a faggot
Contradiction, therefore 0.9999...=1
QED

>he doesn't understand limit theory

Weird how that works

>he misapplies limit theory.

No further proof for existence of infinity needs to be made other than existence of one.

The limit as the number of digits approaches infinity is equal to one. By definition. That's what limits are for.

.333... equals 1/3
.666... equals 2/3
.999... equals 3/3

If the sum of all positive integers equals -1/12 then math must be somehow broken

But dude they're different numbers

Or you don't understand mathematics.

Thank you.

This.

irreverent

Just saying: Hyperreals work, and 0.999... can be seen as shorthand for 1 - ε, which isn't 1.

>physical interpretation
>why mathematics was created in the first place
This is why schools should have history of mathematics as a required class.

>working with hyperreals
>ever

>he doesn't understand .99999.... =/= 1 isn't an integral part of limit theory for open sets

Why does rounding infinitely long numbers blow everyones minds
We do the same thing with pi and i never see people bitching about it

Because this one is not about rounding, it is _literally_ the same.

There are several non-standard analysis concepts, but come on, Hyperreals, Surreals, etc. are barely ever used.

its close enough to 1 that nobody gives a shit about the infinitesimally small bit at the end so we just call them the same

lier

But this isn't actually true in the sense of the word sum that you know

All of these misunderstandings, whether it's the -1/12 meme or the 0.999 =/= 1 meme or a billion other things is just people applying their grade school level of understanding to concepts that are addressed by real math.

>its close enough to 1 that nobody gives a shit about the infinitesimally small bit at the end so we just call them the same
No, it is just one. That's how the real numbers work.

1/3 = 0.3 recurring
2/3 = 0.6 recurring
3/3 = 0.9 recurring = 1

sorry

sounds like you don't "fully understand" basic fractions and decimals mate

for what purpose? 0.9~ is equal to 1.0 for 98% of practical uses.

0.999... + 0.0...1 = 1
0.0...1 = 0
0.999... + 0 = 1
0.999... = 1

A simple proof:
[math]
X = 0.\bar{9}
10X = 9.\bar{9}
10X - X = 9.\{bar} - 0.\bar{9} = 9\
10X - X = 9X
X = 1
[/math]

\(X = 0.\bar{9}\)
\(10X = 9.\bar{9}\)
\(10X - X = 9.\{bar} - 0.\bar{9} = 9\)
\(10X - X = 9X\)
\(X = 1\)

Easy: not formating apparently
X = 0.999
10X = 9.999
10X - X = 9.999 - 0.999 = 9
10X - X = 9X
X = 1