Is 1 Really Equal to .9999999999999999999?

[Demodocus]

1= .9999999999999999999...

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.

 

[mezarashi]

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

 

[Gokul43201]

Here, read this thread COMPLETELY.

https://www.physicsforums.com/showthread.php?t=5513&highlight=.999

 

[HallsofIvy]

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.