Re: back to the roots
Bill,
A practical situation in which I can see infinitely precise inputs is
when developing an interval library routine for evaluating some nasty
function, such as the special functions of mathematical physics, or
even fast and sharp interval library routines for elementary
transcendental functions.
Your previous argument shows that such a library is of purely academic
interest.
Let us assume that all data is only accurate to at most 4 decimal
digits. The number x :=10010 then represents any value in [10005,
10015), so that sin(x) is only known to lie inside [-1,1]. Any attempt
to compute sin(10010) more accurately is "not helpful, and can be
dangerous".
Obviously, a practical interval standard could be much simpler that the
one under development.
Regards,
Markus