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. YHL