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Re: infinities reformulated

 | Date: Tue, 31 May 2005 10:59:56 +0900
 | From: Alex Shinn <alexshinn@xxxxxxxxx>
 | It cannot be "unlimited" in the sense that it is at least memory
 | limited.  No matter how much memory you have, you can never exactly
 | represent the square root of 2 with a floating point representation
 | - that is the definition of irrational ...
 | But your original statement was "arbitrarily big," not "unlimited,"
 | and this should be allowed.  Infinity in this case could be defined
 | as the range of all real numbers greater than the largest possible
 | BigFloat using all of memory for the exponent.

Very clever!  You have rescued the "6.2.2x Inexactness" section (from