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

[Carey Evans]

graham at sloth.math.uga.edu (Graham Matthews) writes:

> I am not sure I understand this. Surely the set of strings on a finite
> alphabet is countable.

[snip]

I think I get it now.

Imagine an alphabet consisting of the characters `0' to `9'.  Now map
this onto decimal numbers like "x1.x2x3x4...xn...", where the length
is infinite.  Some of these are 1, 1.3333..., 1.5, 2, 2.718281828...,
3.14159265....

e and pi are transcendental, and are not rational numbers, so (waving
hands) the set of infinite strings over this alphabet is not aleph-0.
(Although I'd like to know how to expand that above 9.999....)

-- 
	 Carey Evans  http://home.clear.net.nz/pages/c.evans/

	     "I'm not a god.  I've just been misquoted."