Alex Shinn wrote:
 >On 5/31/05, Chongkai Zhu <xxxxxx@citiz.net> 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
xxxxxx@bothner.com   http://per.bothner.com/