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PI Compression

>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.

For those of you without a math background, this means "They all just
don't fit."