On Mon, 20 Nov 2000, Marcus Smith wrote:

> H. S. Teoh wrote:
> >Hmm. This could be a punny fun, too. Um, I mean, a funny pun. :-) Q *is*
> >full of "wholes" -- whole numbers, as well as "holes", the missing
> >irrationals. [Tangential random thought:] In fact, you could just as well
> >say that Q is almost completely filled with holes, with an occasional
> >rational or two, because the cardinality of the irrationals is much larger
> >than the cardinality of Q (infinitely larger, to abuse the term a bit)!
> >So, rationals are actually mere needles in an infinitely large haystack...
> >go figure. :-P
> I have the same problem with my cats, but only on Tuesdays.

<laugh>  Well--that's what I love about infinities.  Thinking about them
gives me the same kind of feeling that looking at the stars does.  (This
is good, BTW.)

> (I stopped understanding this math thread long ago.)

<wry g>  I didn't understand a whole stretch of it; I've never really
formally been introduced to nonstandard number theory--at least not in
enough detail for it.  But I did get the Cauchy sequence bit, which gave
me a headache when I first saw it in analysis (my first theoretical math
course), but was quite beautiful once my brain broke down and gave in.