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Davidthegreattwo
Joined: Fri Mar 06, 2009 1:45 am
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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?
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Mon Apr 23, 2012 11:39 pm |
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Visorak
Team:
Main: Radia
Level: 1101 Class:
Speed Demon
Joined: Wed Oct 10, 2007 6:04 pm Location: q3dm17
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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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seanla4350
Team:
Main: Thermal
Level: 3024 Class:
Engineer
Joined: Sat Jan 16, 2010 2:23 pm
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Re: 0.999...
Don't worry, I got enkelin on this!
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Mon Apr 23, 2012 11:47 pm |
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kanescreed
Member
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Main: Qlimax
Level: 1753 Class:
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Joined: Fri Feb 12, 2010 9:28 am
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Re: 0.999...
lol enk to the rescue!
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Mon Apr 23, 2012 11:49 pm |
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Davidthegreattwo
Joined: Fri Mar 06, 2009 1:45 am
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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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kanescreed
Member
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Main: Qlimax
Level: 1753 Class:
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Joined: Fri Feb 12, 2010 9:28 am
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Re: 0.999...
well one thing that obvious is .999 is .999 and 1 is 1 :p
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Mon Apr 23, 2012 11:52 pm |
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anilv
Member
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Main: enkelin
Level: 3002 Class:
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Joined: Wed Aug 01, 2007 12:28 pm
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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.
_________________ (DefQon1) use a Rhino reconstruotereatarerer - (Pasta) I need to figure out how to get rid of this UrQa Suqqa Ukuk (Bluenoser) Put your finger in your mouth and gag reflex should do the rest
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Mon Apr 23, 2012 11:54 pm |
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kanescreed
Member
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Main: Qlimax
Level: 1753 Class:
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Joined: Fri Feb 12, 2010 9:28 am
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Re: 0.999...
but isnt it .000000000000000000~~~~01 away from 1? lol
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Mon Apr 23, 2012 11:57 pm |
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anilv
Member
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Joined: Wed Aug 01, 2007 12:28 pm
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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.
_________________ (DefQon1) use a Rhino reconstruotereatarerer - (Pasta) I need to figure out how to get rid of this UrQa Suqqa Ukuk (Bluenoser) Put your finger in your mouth and gag reflex should do the rest
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Mon Apr 23, 2012 11:58 pm |
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Nuromishi
Team:
Main: Nuroshounin
Level: 833 Class:
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Joined: Sat Aug 21, 2004 6:48 pm Location: Hoboken, NJ
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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.
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Tue Apr 24, 2012 12:00 am |
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kanescreed
Member
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Main: Qlimax
Level: 1753 Class:
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Joined: Fri Feb 12, 2010 9:28 am
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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. damn. this sir, is some RL hacks right here.
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Tue Apr 24, 2012 12:02 am |
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SkyTitan
Joined: Thu Jul 22, 2010 10:12 pm
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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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Griffin
Team:
Main: Stabberz
Level: 2153 Class:
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Joined: Sat Mar 03, 2007 10:55 am
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Re: 0.999...
I have a diagram for things like these.
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Tue Apr 24, 2012 6:11 am |
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thijs12b
Member
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Joined: Sun Nov 07, 2010 8:08 am
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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 This also counts for 0.9999999x2 etc!
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Tue Apr 24, 2012 6:37 am |
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Nuromishi
Team:
Main: Nuroshounin
Level: 833 Class:
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Joined: Sat Aug 21, 2004 6:48 pm Location: Hoboken, NJ
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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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