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Unread 18-04-2004, 22:49
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Re: .999~ = 1

alright i thought of a different way to prove that .999...=1

first we have to prove that if (X+Y)/2=X or (X+Y)/2=Y then X=Y
this is simple

(X+Y)/2=X
X+Y=2X
0=X-Y
Y=X

alright now we move on

1 (.9999...+1)/2 ?= .999...
2 (1.999...)/2=
3 .999...=.999...
now you might be thinking: "whoa...how do you get from 2 to three...that looks crazy"

well 1.9/2=.95
1.99/2=.995
1.999/2=.9995

so 1.999.../2=.999...5

however i have given all you non believers false hope with that last 5

1.999.../2=.999...

because the nines will go on FOREVER, they wont stop, so that five does not exist the five never happens because the nines never stopped...thus .999...=1
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