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

[Chad Netzer]

Hmmm, I replied to the earlier thread before seeing these responses (my newsreader
put these in a new thread).  So, I'll respond to several posts here:

Gordon McMillan wrote:

> > Chad Netzer wrote:
> > >  So, there are infinitely more strings which start with underscores than do not,

> Unfortunately, Chad mispoke.

Perhaps, but remember, the original statement was that "The subset of infinity that
does not start with an underscore is exactly 50%."  I simply wished to express
the "infinitude" of infinity without getting too formal (In my last post, I even
"disproved" my own statement just as you did).  Introducing Cantor's theories
helps resolve these apparent paradoxes.

> Chad's trickery is in trying to get you to assume that Aleph-nough
> minus Aleph-nought is 0. Nice try.

Trickery?  Now that hurts. :-)  I left out Aleph, originally, since I didn't plan to be so
formal responding.  (Besides, my evil plan nearly worked, Muhahahahaha)

In another reply, Moshe Zadka wrote:

> OK, here it is: all infinite sets of strings are of power aleph null,
> which is the same as that of the natural numbers.

    Surely Cantor's original proof showed that the set of all infinite length strings
(what I assume you mean by 'infinite sets of strings') with a finite alphabet, is size
aleph-1.  All infinite strings of binary digits (0110101001....) cannot be paired
one-to-one with the natural numbers  (there are 2**infinity possible strings,
which is aleph-1, while the natural numbers are aleph-0)

> Any future discussions should be moved to sci.math, where the participants can
>  be properly flamed for not having a clue in set theory <0.5 wink>

aleph-null or aleph-one: which is the number of ways I can express my regret
for a zero-Python-content posting?

Cheers,
Chad Netzer
chad at vision.arc.nasa.gov