Re: .99999... still=/= 1

From: John Savard (jsavard_at_excxn.aNOSPAMb.cdn.invalid)
Date: 12/18/04 

Date: Sat, 18 Dec 2004 10:16:20 GMT

On 16 Dec 2004 01:38:18 GMT, smart1234@aol.com (S. Enterprize Company)
wrote, in part:

>.999... only approaching 1, it doesn't equal 1.

It would seem that way.

But appearances can be deceiving.

It is certainly possible to use .999... as a symbol for a quantity that
only approaches 1 as a limit. But that isn't its normal meaning.

Because if we did that, then .1111.... wouldn't equal 1/9.

Essentially, _if_ .999... stands for a real number, then it stands for
the real number 1. Because any real number that doesn't equal 1 differs
from 1 by a *finite* amount.

The distinction between x=1 and x approaching 1 as a limit is an
important one in mathematics, but numbers written in decimal form are
not used to indicate this distinction; they are only used to indicate
numbers.

John Savard
http://home.ecn.ab.ca/~jsavard/index.html

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