Re: Is 0.123... a member of the set {0, 0.1, 0.12, 0.123, ...}?

From: robert j. kolker (nowhere_at_nowhere.net)
Date: 02/01/05 

Date: Tue, 01 Feb 2005 07:14:07 -0500

The World Wide Wade wrote:
>
> But .099999999..... has infinitely many non-zero digits after the
> decimal point, and it's in the set {0, 0.1, 0.12, 0.123, ...}.

Irrelevent. 0.0999.... converges to a rational number. The number 0.123
etc is not a repeating decimal so it converges to an irrational number.
All the elements of the set {0, 0.1, 0.12, etc} are rational numbers.

Bob Kolker

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