# 1= .9999999999999999999.........

by Demodocus
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 P: 7 Here it is... 1/3= .33333333333........... 2/3= .6666666666......... so 3/3= .9999999999....... so 1= .999999999........ Wtf? I think that this "paradox" means that there is a problem with our definition of infinity. At least, the definition needs to be refined. Does this mean that 1 is not equal to one, or is .9999999... another name for one? I think this topic needs to be adressed.
 HW Helper P: 661 Oh no, I remember a long one discussing this. Something about convergence, but I'll sit back and watch :)
 Emeritus Sci Advisor PF Gold P: 11,154 Here, read this thread COMPLETELY. http://physicsforums.com/showthread....highlight=.999
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PF Gold
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## 1= .9999999999999999999.........

Ouch! Another one. Demodocus- there is nothing wrong with "our" definition of infinity (actually, I can't speak for yours). Yes, 0.9999.... is just another name for 1 (that, I must say, is put very nicely). Our definition of "base 10 enumeration system" is such that 0.9999.... means the sum of the infinite series 9/10+ 9/100+ 9/100+ ... which is a geometric series that can be shown to converge to 1.