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

[Graham Matthews]

Gordon McMillan (gmcm at hypernet.com) wrote:
: Moshe, Chad & I straightened this out in email. Chad is correct 
: (well, if you take him as saying "more than Aleph-0").
: 
: Instead of the integers, take the numbers between 0 and 1. Use your 
: mapping. Now realize that most of the numbers you've created are 
: transcendentals, and the rationals, by comparison, amount to a hill 
: of beans. So it _is_ a denser form of infinity than the integers.

I am not sure I understand this. Surely the set of strings on a finite
alphabet is countable. Indeed the set of strings on a finite alphabet
is the countable union of a collection of finite sets. For each n
we have the set of all strings of length n (a finite set since the
alphabet is finite), and then we take the union over n of all such
sets. So I am not really sure what you are saying here?

graham
-- 
             Like a bird on a wire
        Like a drunk in a midnight choir
            I have tried in my way
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