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Topic: 0 to the power 0
Replies: 26   Last Post: Nov 11, 1996 8:36 PM

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roitman@oberon.math.ukans.edu

Posts: 243
Registered: 12/6/04
Re: 0 to the power 0
Posted: Nov 11, 1996 6:20 PM
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Ted Alper writes:
>
>For that matter, one doesn't have to bring up even the non-standard
>reals to distinguish "0.999..." from 1 -- you can do this and define a
>perfectly good total order on the set of all decimal expansions (it
>is, in effect, a Cantor set).


This is using base 11 expansions, where the largest possible digit is not
allowed. In particular, it is changing the arithmetic meaning of .9999..
as a number > 9/10, > 99/100, etc. I.e., it is changing the rules of the
game at the elementary (= first order logic) level, which doesn't quite
seem fair.

Cheers.

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