Is 1 Really Equal to .9999999999999999999?

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SUMMARY

The discussion confirms that 1 is indeed equal to 0.9999999999... through the mathematical principles of infinite series and convergence. Specifically, the series 9/10 + 9/100 + 9/1000... is a geometric series that converges to 1. Participants emphasize that this equality is a consequence of the base 10 enumeration system and does not indicate a flaw in the definition of infinity. The conversation highlights the need for clarity in understanding these mathematical concepts.

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  • Understanding of infinite series and convergence
  • Familiarity with geometric series
  • Knowledge of base 10 enumeration system
  • Basic principles of mathematical equality
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Demodocus
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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.
 
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Oh no, I remember a long one discussing this. Something about convergence, but I'll sit back and watch :)
 
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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