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


by Demodocus
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Demodocus
Demodocus is offline
#1
Oct7-05, 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.
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mezarashi
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#2
Oct7-05, 10:19 PM
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P: 661
Oh no, I remember a long one discussing this. Something about convergence, but I'll sit back and watch :)
Gokul43201
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#3
Oct7-05, 10:49 PM
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PF Gold
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Here, read this thread COMPLETELY.

http://physicsforums.com/showthread....highlight=.999

HallsofIvy
HallsofIvy is offline
#4
Oct8-05, 08:03 AM
Math
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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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