Re: math : the problem with points.

On 2008-04-05, Julio Di Egidio <julio@xxxxxxxxxxxxx> wrote:
If we get into the domain of computable numbers (actual numbers),
and take closed interval arithmetic as reference, that lower limit
(actually) exists and it is the floating-point limit to underflow,
intrinsic to any specific implementation. It is, in fact, under all
respects, a rational number.

No, there are plenty of computation systems that have no such element
and do not have underflow. Exact arbitrary-precision rational
arithmetic, for example.

There are even systems that can handle some exact irrationals and even
transcendentals.

Fixed-precision floating point numbers are just one system that has
fast hardware support in practice, and certainly doesn't define all
computational possibilities.


- Tim
.

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