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Re: infinities reformulated



Alex Shinn wrote:
>On 5/31/05, Chongkai Zhu <mathematica@xxxxxxxxx> wrote:
And your statement "the precision of an inexact (or exact) number
representation cannot be unlimited" is wrong. For example, Mathematica
implements "unlimited precision number", although it may have some
flaws.


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

The message you quoted did not say "floating point".  There are finite
ways of representing trancendentals.  "The square root of 2" is one.
A more interesting apprach is to use continued fractions.
For example see http://portal.acm.org/citation.cfm?id=31986
(I don't remember if they use continued fractions.)
--
	--Per Bothner
per@xxxxxxxxxxx   http://per.bothner.com/