while (a=b()) ... infinite sets digression
Gordon McMillan
gmcm at hypernet.com
Wed May 19 00:55:04 EDT 1999
Greg Ewing wrote:
> Chad Netzer wrote:
> >
> > So, there are infinitely more strings which start with underscores than do not,
>
> Hmmm... this would seem to imply that there are
> infinitely many more strings starting with any
> given character than any other character.
>
> Which seems absurd. Although where infinities
> are involved, that doesn't necessarily mean it's
> not true...
>
> Tricky and dangerous beasts, these infinities!
Unfortunately, Chad mispoke. For any string beginning with an
underscrore there are (num_possible_characters-1) strings not
beginning with an underscore (just replace that first character).
But if there are Aleph-nought strings beginning with underscore,
there are N*Aleph-nought == Aleph-nought not beginning with
underscore.
Chad's trickery is in trying to get you to assume that Aleph-nough
minus Aleph-nought is 0. Nice try.
All this assumes, of course, that you allow strings of infinte
length. Personally, I don't. And since strings don't have sides, you
can't even fake one by folding a finite-lengthed one into a Mobius
string.
though-some-forms-of-Unicode-come-close-ly y'rs
- Gordon
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