interval X**Y and exceptions generally

[David B. Serafini]

> Date: Wed, 01 Apr 1998 18:46:06 +0200
> From: Arnold Neumaier <neumacma.univie.ac.at>

> [...]
> I find nothing bad about this. Continuity is not relevant for floating
> point operations; we also do not mind that x/x=NaN when a positive x
> underflows to 0. We also don't signal an error if (exp(x)-1)/x vanishes
> for small x after seemingly converging to 1 as x approaches 0. Every
> mathematician is made familiar with such continuity failures in 
> finite precision arithmetic.
> [...]
>
> Arnold

This is a great example of the classic "intuition gap" between mathematicians
and scientists/engineers.  I venture to guess that many if not most
s/e programmers would be very surprised by such continuity failures.
And very few would ever consider anticipating them before they happened.

David   <dbsanersc.gov>