Thread: .999 = 1?
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Old 08-04-2012, 01:54 AM
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septimus is offline
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Originally Posted by TriPolar View Post
One thing I learned was that there are no other numbers between .999... and 1. That means they are the same number.
This assumes a property of "number." Note that if by "number" we mean "integer" then there is no "number" between 16 and 17 yet they are unequal.

I find it best, if only "for old time's sake" , to appeal to the Axiom of Archimedes, which can be paraphrased as
  For any positive ɛ there is a finite integer N such that Nɛ > 1

Notice that for any N, you can make N(1 - 0.999...) < 1 by providing sufficiently many 9's.

Last edited by septimus; 08-04-2012 at 01:55 AM.