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Point nine recurring equals one

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Fire Elemental (18)	Point nine recurring equals one - 2006-02-27 08:04:14
Registered: unknown Posts: 21	Since nobody is using this forum, I have decided to seed the roots of conversation. Does 0.9999... == 1? Discuss.
Dennis (13)	Point nine recurring equals one - 2006-02-28 06:26:16
Registered: unknown Posts: 13	Everyone knows this \"proof\": x = 0.9999... 10x = 9.9999... 9x = 9.9999... - 0.9999... = 9 x = 1 :P
Fire Elemental (18)	Point nine recurring equals one - 2006-03-02 06:50:29
Registered: unknown Posts: 21	I think the real issue in this classic problem is whether or not 0.9999... is actually a real number. According to my memory of grade school fractions, decimal numbers are just representations of decimal numbers. As far as I know, there is no fraction that evaluates out to 0.9999...
C172 (101)	Point nine recurring equals one - 2006-03-07 09:51:20
Registered: unknown Posts: 5	It has been brought to my attention that 00111111100000000000000000000000 equals 1.
Dirtysouthafrican (2)	Point nine recurring equals one - 2006-03-07 10:47:01
Registered: unknown Posts: 312	0.99999... = 1 That is because 0.9999... is defined to be `lim K->inf sum{n=0...K} (9/10) 10^{-K} = (9/10) * lim K-> inf sum{n=0...K} 10^{-K} = (9/10) * (10/9) = 1` Therefore the statement that \"there is no fraction that evaluates out to 0.9999...\" is false... 1/1 obviously evaluates out to 0.9999... because 0.99999... is DEFINED as a limit of a series and the series converges to 1 therefore it\'s limit is 1 therefore 0.9999999... is defined to be 1.

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