Math Forum

From: haoyuep@aol.com (Dan Hoey)
Date: May 2, 2004 11:32 AM
Subject: Re: Order type of English names of natural numbers

On 29 Apr 2004, Stewart Gargis wrote:

>But at least we can show your set is well-ordered, because it's a
>subset of the set of all strings over a finite alphabet, which is
>well-ordered in the lexicographical ordering (since otherwise there
>would be a decreasing chain of words, not possible when the space
>sorts first).

What about the sequence ab, aab, aaab, aaaab, ... ?  I think you need
to do something like sort the strings by length before lexicographic
order to make them a well-ordered set.  But I don't see anything that
makes the sort order of the space significant.

Dan Hoey
haoyuep@aol.com