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The5thCandidate · 05-27-2004, 12:49 PM

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

05-27-2004, 12:49 PM	#11 (permalink)
The5thCandidate Crazy Location: East coast of Canada	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 __________________ Muthtard?! Don't let'th be thilly. Lemon, now that'th different...