1= .9999999999999999999.........by Demodocus Tags: None 

#1
Oct705, 10:16 PM

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. 



#2
Oct705, 10:19 PM

HW Helper
P: 661

Oh no, I remember a long one discussing this. Something about convergence, but I'll sit back and watch :)




#3
Oct705, 10:49 PM

Emeritus
Sci Advisor
PF Gold
P: 11,154





#4
Oct805, 08:03 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,886

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.



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