Thread: Does 0.9 repeated = 1?

Are you going to try to tell me that something infinitely close to 1 isn't 1?

Originally Posted by Kushna Mufeed

Are you going to try to tell me that something infinitely close to 1 isn't 1?

yes

Prove it

Originally Posted by Kushna Mufeed

Prove it

for practical examples, 0.9 recurring does equal 1, because machines have a fixed amount of space in which to store a value

give it an irrational number like 0.9 recurring, and it'll fill up the space, and still have a remainder, so it'll round up to 1, but this is not accurate

0.9 recurring is, by definition, a number that infinitely reaches towards 1 but never gets there.
So that question really has no place.

No one asks whether 1 equals to 2...we know that each is a different number by definition, as it were. So why ask whether 0.9 recurring (that very number) equals to 1 (a different number) if you've just spoken about two different numbers? Not variables but different real numbers.

Just because it's used as equaling 1 for calculations doesn't make it precise and true. Sounds ridiculous but...you can't argue with the number's very definition, and apparently people prefer actually finishing their calculations rather than sitting there at a dead end unable to work with an irrational number that never ends.

I hate math though, so I'm just going at this from a logical point of view. Definitions are axioms!

another way to look at it

0.15 is a rational number
but write that in hex, and you get 0x0.2666666.....
an irrational number

a rational number in one base can be irrational in another
and vice versa

there will likely be some base where decimal 0.9 recurring is rational
and therefore easily shown that it is not equal to 1

Originally Posted by Merlock

0.9 recurring is, by definition, a number that infinitely reaches towards 1 but never gets there.

Actually, 0.9~ is by definition equal to 1 because of the axiom that every real number has two representations; in this case 1.0~ and 0.9~.

Yes.

EDIT: xD Ynot got to it first!

0.9 recurring is, by definition, a number that infinitely reaches towards 1 but never gets there.
So that question really has no place.

No one asks whether 1 equals to 2...we know that each is a different number by definition, as it were. So why ask whether 0.9 recurring (that very number) equals to 1 (a different number) if you've just spoken about two different numbers? Not variables but different real numbers.

Just because it's used as equaling 1 for calculations doesn't make it precise and true. Sounds ridiculous but...you can't argue with the number's very definition, and apparently people prefer actually finishing their calculations rather than sitting there at a dead end unable to work with an irrational number that never ends.

I hate math though, so I'm just going at this from a logical point of view. Definitions are axioms!

Actually, you're wrong. Firstly, people have asked for a proof that 1 does not equal 2, and all the other stuff assumed in arithematic.

1=0.9999...
http://en.wikipedia.org/wiki/0.999...#Proofs

It has been proven, look above. Also, 0.9999.. by definition is not irrational.

See 1/3=0.3333....., then you times it by 3/3=0.9999....

Actually, even if you couldn't do that it still has a repeating digit, which proves it can't be irrational, as the definition of a irrational number is that there is no repeating digit in sequences of numbers in n-1 turns. For example you don't get stuff like 2.12222..., this would have a repeating 2, so wouldn't be irrational. 0.999.. has repeating 9 so is not irrational.

P.S. Seriously, don't do mathematics.

there will likely be some base where decimal 0.9 recurring is rational
and therefore easily shown that it is not equal to 1

It has been mathematically prove, look above. That 0.9999... =1, so its a fact or a theorem in this case.

Wrong.

y = x^3 / x - 5(.999~)

If 1 = .999~ then y would be undefined at x = 5. When x = 5, that equation equals -5. You have to use limits to show it, but it's -5, not undefined.



Limits is a weird thing. Those proofs are correct on wiki, however you can also prove that they don't work. This happens a lot with limits and calculus.

the (1/9) x 9 proof was proven inaccurate

it's essentially using a property of mathematics to disprove that same property

there's a counterpoint that says,
it should be written as (I'm paraphrasing)

(1 / 8.999999.....) x 8.99999.....

which is not possible to do (with absolute accuracy)
so 0.99999.... cannot equal 1

The problem with numbers is that people look at them differently depending on how they are used. Not in terms of rounding, just in terms of how they get used in calculations.

Does .999~ = 1?
Computers - yes
Physics - yes
Relativity Physics - no
Math - no
Calculus - yes

Does -0 = 0? (another common dispute)
Computers - no
Physics - no
Relative Physics - no
Math - yes
Calculus - yes

If you'd like I can give examples of all of these.

Originally Posted by ninja9578

The problem with numbers is that people look at them differently depending on how they are used. Not in terms of rounding, just in terms of how they get used in calculations.

Does .999~ = 1?
Computers - yes
Physics - yes
Relativity Physics - no
Math - no
Calculus - yes

Does -0 = 0? (another common dispute)
Computers - no
Physics - no
Relative Physics - no
Math - yes
Calculus - yes

If you'd like I can give examples of all of these.

Wait, what?

I thought -0 = -1(0) = 0

And technically, .3333...(3) doesn't equal 1, but 1/3(3) does.

Limits is a weird thing. Those proofs are correct on wiki, however you can also prove that they don't work. This happens a lot with limits and calculus.

Proof doesn't work. Seriously, are you some sort of mathematical crank.

A proof is a proof, it has been proven. It is a theorem, it is a fact. Anyway, the only thing strange is that

Tom Apostol concludes,

The fact that a real number might have two different decimal representations is merely a reflection of the fact that two different sets of real numbers can have the same supremum

it's essentially using a property of mathematics to disprove that same property

there's a counterpoint that says,
it should be written as (I'm paraphrasing)

(1 / 8.999999.....) x 8.99999.....

Firstly, NO. 9.99999=10, not that 8.999999=10.

So lets 1/1=9/9, everything is okay, then we have 9x1/9=1, then we have
9x 0.111...=1, therefore 0.99999=1.

Anything divide by something is 1, so how is that a counterpoint?

Lastly, it has been prove by analysis, so there. Look at the bottom of the wiki article.

Math - no
Calculus - yes

Calculus is mathematics, also you can use analysis to prove it. So what are you basing you're assumptions on. It has been proven in mathematics that 0.99999...=1.

You can prove it using constructionism, which is most concrete form of mathematics. You can construct it from the real numbers, or prove it by dedekind cut.

Wow, I used to think Ynot was an intelligent person. And here he is saying that .99... does not equal 1.

It does.

There are numerous proofs that .99... equals 1. How many proofs are there that it does NOT equal 1? Zero. There are no such counter-proofs.

Here is a proof. Try to think of a number between .9999... and 1. Thought of a number? No? That's because there are no numbers between .999... and 1. You know why? Because they're the same number. If they were not, then there would be a number between them.

This isn't rocket science. I've known this since middle school.

http://polymathematics.typepad.com/p...sorry_it_.html
One of many sites that you could learn from.

PS: Please stop posting your flawed mathematics in this thread. It is an embarrassment. Ynot, stop posting here unless you cure your ignorance.

See my post above about multiple views.

Computer science says that 1/∞ = 0 so 1 - 1/∞ = 1
Physics says the same thing because it uses limits to reach asymptotes
Relative physics uses calculus which can reach asymptotes, but doing so causes failure among basic physics so the break down of physics is what says that .999~ != 1, not the math.
Simple math states that asymptotes can not be reached, therefore .999~ != 1
Calculus can use limits to reach as asymptotes

Originally Posted by ninja9578

See my post above about multiple views.

Computer science says that 1/∞ = 0 so 1 - 1/∞ = 1
Physics says the same thing because it uses limits to reach asymptotes
Relative physics uses calculus which can reach asymptotes, but doing so causes failure among basic physics so the break down of physics is what says that .999~ != 1, not the math.
Simple math states that asymptotes can not be reached, therefore .999~ != 1
Calculus can use limits to reach as asymptotes

This has nothing to do with physics or computer science, this has to do with MATHEMATICS and the FACT that .999 repeating is EQUAL TO ONE.

Relative physics uses calculus which can reach asymptotes, but doing so causes failure among basic physics

Please get SOME idea of what you're talking about and stop posting bullshit.

Simple math states that asymptotes can not be reached, therefore .999~ != 1

.999... IS NOT AN ASYMPTOTE. IT IS A NUMBER. ONE WHOLE NUMBER.

Just like 1 is not an asymptote, 3 is not an asymptote, .5 is not an asymptote.

Does 3.0000... not exist because the number's an asymptote? Is that number "going anywhere"?

failure among basic physics so the break down of physics is what says that .999~ != 1, not the math.
Simple math states that asymptotes can not be reached, therefore .999~ != 1
Calculus can use limits to reach as asymptotes

Mathematics says you can do a dedekind cut and then show that 0.9999...=1. There is various mathematical proofs that this is true. Go look at the wiki article. Also, you can prove it by constructing the real numbers from axiomatic set theory. The point is, there is no counter proof, all you have is faulty reasoning.

Also, do you except that geometric convergence in mathematics, for example 1/2+1/4+1/8+...=1. If so then you except that 0.999...=1. As all you need is r=1/10 and then have

9(1/10)+9(1/10)^2+....=1. Hence all you need to except is geometric convergence, which is accepted within mathematics.

Calculus can use limits to reach as asymptotes

There is something called analysis, seriously do you know any analysis? or how to prove stuff within analysis?

When I discovered this .999 problem it made me realize the true stupidity of rational thought.

If something is infinitely close to something else, isn't it touching it?

No, because the universe doesn't work in a way that makes sense. When do we get to do it over again?

if 0.999~ = 1
does, 0x2.666~ = 0x2.7
?

Some dude that studies math I know said it was mathemathically provable. Then again, what does he know. Then again, who cares. Then again, I hardly ever order 0.9999...99 pancaces in a restaurant.

Originally Posted by Neruo

Some dude that studies math I know said it was mathemathically provable. Then again, what does he know. Then again, who cares. Then again, I hardly ever order 0.9999...99 pancaces in a restaurant.

There have been like a dozen proofs in this thread already. Get your head out of your ass.

Originally Posted by drewmandan

There have been like a dozen proofs in this thread already. Get your head out of your ass.

Excuse me? (also: Proof? Where?)

Of course I didn't read all the posts in this topics. Also, yeah, probably I didn't really say anything new. Then again, if all the things on the internet had to be new, then this entire topic shouldn't exist.

Also, for practical reasons, anyone that honestly cares in his day-to-day life that 0.999999 = 1 is a faggot.

So lighten up.

Originally Posted by Neruo

Also, for practical reasons, anyone that honestly cares in his day-to-day life that 0.999999 = 1 is a faggot.

0.999999 does not equal 1.

And you, sir, are the one that is calling people names.