Asmus Freytag scripsit:But what if you use a null terminated string, and precede it with decimal digits (what's a bit of inefficiency when you are talking about infinity?) or any encoding in which null is not a valid part of the number? Then the precision is truly infinite, surely (at least to the first transfinite number), except that if the universe is finite there is an ultimate limit on storage capacity.
PS: private answer to Jill: make sure that your characters are always represented internally by infinite precision integers.
Actually, the intractability of the transfinite ordinals shows us that there can be no such thing. Ordinary "infinite precision" integers begin with a fixed-size length word saying how many words (for whatever definition of "word") follow. But eventually the fixed-size length word will overflow, and must be replaced by a variable-sized length word, itself prefixed by a length^2 word. But eventually the length^2 word will overflow, and must be replaced .... But eventually the number of length words will become too large, and the length-length word will overflow, requiring ... But then ...
You can't win.
It all reminds me of a book I read, not intended as science fiction but as a real contribution to science and philosophy, which predicted that the universe would collapse but as it collapses be converted into a giant computer whose speed would increase exponentially (or something) as it collapsed in such a way that in the finite time before the collapse it could perform an infinite number of calculations. Which had some rather interesting consequences, but they go well off topic!
-- Peter Kirk [EMAIL PROTECTED] (personal) [EMAIL PROTECTED] (work) http://www.qaya.org/
