while (a=b()) ... infinite sets digression

[Chad Netzer]

Gordon McMillan wrote:

Flame-bait, which I refuse to take, and the following statement.

> > In fact, both are probably Aleph-1 sets which
> > means they are larger than the set of integers...  I'm out of my
> > area, here, so I'll let it go at that. ;)
>
> Ay yi yi. They are countable (Aleph-0). Proof: you can sort
> them. In fact, using an insertion sort, I can sort them a
> _whole_lot_faster_ than you can create them. (See what happens when
> you compare infinities?).

I'm sorry I didn't use formal definitions from the start of this thread; it
would have caused less confusion.  In response to the above, and as I said in
my last post,  the set of all infinite length strings (with a finite alphabet) is
size aleph-1;  they cannot be counted (or even sorted completely).  Cantor
proved this and I won't waste your time proving it here (although it is a
short and wonderful proof).   My example was in reference to this set (plus
all finite length strings).  So if I expressed things in a way that caused
confusion, especially to "Mr. Set Theory" McMillan, I apologize.

> thank-god-it-doesn't-take-set-theory-to-launch-a-shuttle-ly y'rs

uhhh, yeah.

Chad Netzer