pi compression

[Do you know what's in the trunk? 25-May-1993 0917]

>
>>Since all possible finite bit strings are, by definition, contained
>>in the unending cavalcade of bits in pi, 
>
>Definition?  I have seen not this asserted even by theorem.  Not
>surprising, since the statement is patently false.  There are
>2^{\aleph_0} finite bit strings, and only \aleph_0 of those are
>subsequences of pi.

Um, it doesn't follow to me that it's _obvious_ that 2^Aleph_0 is
larger than Aleph_0.  

It might be- but I'd like to see the proof.

Now, Aleph_0 ^ Aleph_0, on the other hand...

	-Bill (wondering why this thread of recursively nonenumerable
		transfinite ordinal stuff keeps cropping up in *all* his
		mailing lists)