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Post 0.999...
Is 0.999 recurring = to 1?
I think it is but I'm not sure now so id like some opinions.
I know it can be proved by:
x=0.9recurring
10x=9.9recurring
9x=9
Therefore x=1
And that 1-0.9recurring is just lots of zeroes, so many that the one at the end is so far away that it doesn't exist cos it can never be written.
What do you guys think?


Mon Apr 23, 2012 11:39 pm
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Post Re: 0.999...
Davidthegreattwo wrote:
x=0.9999...
10x=9.9999...
9x=9

Therefore x=1

... is shorthand for recurring btw.

I highlighted the part that I don't understand. Are you trying to subtract 1 there?

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Mon Apr 23, 2012 11:45 pm
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Post Re: 0.999...
Don't worry, I got enkelin on this!


Mon Apr 23, 2012 11:47 pm
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Post Re: 0.999...
lol enk to the rescue!


Mon Apr 23, 2012 11:49 pm
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Post Re: 0.999...
yeah I should have done:
10x-x=9.9...-0.999...
to make it more clear

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Mon Apr 23, 2012 11:51 pm
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Post Re: 0.999...
well one thing that obvious is .999 is .999 and 1 is 1 :p


Mon Apr 23, 2012 11:52 pm
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Post Re: 0.999...
Yes, they are the same thing. This is not an opinion but the simple fact. To avoid getting too technical in a first post, let me put this to you: two numbers are by definition identical if there is no other number that is greater than one of them and less than the other. You can probably convince yourself that this is the case for .9 repeating and 1.

The proof you posted looks right, but I didn't read it very carefully.

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Mon Apr 23, 2012 11:54 pm
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Post Re: 0.999...
but isnt it .000000000000000000~~~~01 away from 1? lol


Mon Apr 23, 2012 11:57 pm
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Post Re: 0.999...
kanescreed wrote:
but isnt it .000000000000000000~~~~01 away from 1? lol


If by ~ you mean "repeated infinitely and then put a 1" then that's not a real number. :P

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Mon Apr 23, 2012 11:58 pm
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Post Re: 0.999...
1/3 == .333...
3 * (1/3 ) == 3 * .333...
3/3 = .999...
1 = .999...

There is another way of looking at it. ^

EDIT: Fuck my insertion of excess words.

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Last edited by Nuromishi on Tue Apr 24, 2012 12:04 am, edited 2 times in total.

Tue Apr 24, 2012 12:00 am
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Post Re: 0.999...
anilv wrote:
kanescreed wrote:
but isnt it .000000000000000000~~~~01 away from 1? lol


If by ~ you mean "repeated infinitely and then put a 1" then that's not a real number. :P

damn. this sir, is some RL hacks right here.


Tue Apr 24, 2012 12:02 am
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Post Re: 0.999...
Nah the fractions one doesn't work. There's always something left in the carry. (Whatever the fuck that thing is in long division)

*continues to go through wikipedia's list*
Next one up, digit manipulation. No, sorry, again, you have an infinite amount of carrying you did not do. The idea is that the length is infinite. Multiplying by ten doesn't shift it like they want. Subtle difference, like subtraction and differences, one is always positive there, subtle difference, though. Try it in another base. (should be fun, 0.999... in base two, easy enough, right?)

And, yeah, all of this hinges on how mathematics treats infinity. You might as well outright state that it's true because math says so.

Long story short, the infinite string of numbers part of it is a property of the number and is not supposed to be gotten rid of like that. Kind of like sqrt -1. You can't just skip that(you can if the equation called for difference instead of subtraction though, see relativity for why it matters)

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Tue Apr 24, 2012 1:10 am
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Post Re: 0.999...
I have a diagram for things like these.


You do not have the required permissions to view the files attached to this post.

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Tue Apr 24, 2012 6:11 am
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Post Re: 0.999...
Not giving a fuck 0.999 isn't 1, what you gonna do about it?!?

Here's my proof;

0.999 x 2 = 1.998

1 x 2 = 2

Fuck logic :D

This also counts for 0.9999999x2 etc!

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Tue Apr 24, 2012 6:37 am
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Post Re: 0.999...
SkyTitan wrote:
Nah the fractions one doesn't work. There's always something left in the carry. (Whatever the fuck that thing is in long division)


I would like to see you actually show the error in my lackluster proof.

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Tue Apr 24, 2012 8:03 am
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