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-   -   Does 0.9999(repeating) = 1? (http://forums.na.leagueoflegends.com/board/showthread.php?t=3035994)

Insentience 01-23-2013 10:55 AM

Does 0.9999(repeating) = 1?
 
Me and a friend were having a debate whether or not 0.999... (for those who are confused the 9 is repeating.). I'm saying it does = 1, but he says it doesn't. Though I think I may be right, but there is always the benefit of doubt, and I am open to hearing what others have to say.

So if 0.999... does equal 1, then explain how it equals 1.

but if 0.999... doesn't equal 1, then explain how it doesn't equal 1.

This has been bugging me for awhile.

Sporq 01-23-2013 10:55 AM

It does.

edit: because calculus.

Wulfestopheles 01-23-2013 10:55 AM

Why don't you go ask your math teacher and not a bunch of forum rabble?

Viktorious Alekt 01-23-2013 10:56 AM

You might wanna join a college-level math class to have an answer to that.

Sweagen 01-23-2013 10:56 AM

no it equals 0.999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 9999999999999999999999 not 1

Mèdusa 01-23-2013 10:57 AM

0.9999.... = X
10 X = 9.999....
10X - X = 9
9X = 9
9X / 9 = 1
So, X = 1

That's the standard proof anyway

Eleshakai 01-23-2013 10:57 AM

I read the mathematical reasoning behind this one once, and it was pretty awesome. But the essential truth is that 0.9 repeating does in fact equal 1.

HunterHagen 01-23-2013 10:57 AM

are we in junior high school here?

GZA 01-23-2013 10:58 AM

Are you 15? There is no debate about this, in fact, what you are "debating" is a common exercise used in introductory algebra classes.

If x=0.999..
10x=10(0.999...)
9x=[10(0.999...)] - 0.999
9x=9
x=1

CrazedPorcupine 01-23-2013 10:58 AM

.9999999999999999999999999999999999999999999999999 9999999 etc is incredibly close to one and is usally written as lim of x as x approaches 1 So for most calculations, it does equal one, but not really.


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