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FOR REFERENCE: Any number followed by ~ represents a repeating decimal. (IE: .9~ = .999999999etc)
.9~ = 1
(exactly not approximatley...)
ELEMENTRY PROOF:
.3~ = 1\3
.6~ = 2\3
(1\3) + (2\3) = 1
.3~ + .6~ = .9~
.9~ = 1
ALGEBRAIC PROOF:
x = .9~
10x = 9.9~
10x - x = 9.9~ -.9~
9x = 9
x = 1
x = .9~ = 1
CALCULUS PROOF:
lim(m --> inf) sum(n = 1)^m (9)/(10^n) = 1
0.9999... = 1
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Muthtard?! Don't let'th be thilly. Lemon, now that'th different...
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