Is 1 Really Equal to .9999999999999999999?

  • Context: Undergrad 
  • Thread starter Thread starter Demodocus
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Discussion Overview

The discussion revolves around the mathematical assertion that 1 is equal to 0.9999999999999999999..., exploring the implications of this equivalence and the nature of infinity. Participants examine the convergence of series and the definitions involved in this concept.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asserts that 1 equals 0.9999999999... and questions whether this indicates a problem with the definition of infinity.
  • Another participant recalls a previous discussion related to convergence but does not elaborate further.
  • A third participant provides a link to a prior thread discussing the topic in depth.
  • A later reply states that there is no issue with the definition of infinity and claims that 0.9999... is simply another representation of 1, explaining it as the sum of a converging geometric series.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the equality between 1 and 0.9999999999..., with some asserting it as a settled matter and others questioning the underlying definitions and concepts.

Contextual Notes

The discussion includes assumptions about the base 10 enumeration system and the nature of infinite series, which may not be fully articulated or agreed upon by all participants.

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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