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Re: infinities reformulated

On 5/31/05, Chongkai Zhu <mathematica@xxxxxxxxx> wrote:
> MACLISP is the closest answer. It has exactly what you said and
> called it bigfloats. I searched and find that Perl also implements
> bigfloat as a library.
> 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 - that is the
definition of irrational, you don't even need to go to transcendental numbers
for this.  In fact, irrational literally means "no ratio," and was only later
applied by analogy to imply a lack of reasoning.

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.