On Mon, 2014-04-21 at 14:18 -0400, John Cowan wrote:
> Bear scripsit:
>
> > If you get +inf.0 instead, that's still nonsense (because you multiplied
> > something finite by something finite, mathematically you should have
> > a finite result)
>
> It's not nonsense, actually. Inexact numbers can be interpreted as
> intervals, and +inf.0 can then be identified with the open interval
> (1.79769313486231570e+308, \infty). So when you get +inf.0 from
> multiplying two exact numbers, you are being told with 100% correctness
> that the answer falls into that interval.
>
In asserting that it is not nonsense, you must allow that Scheme
is using the word "infinity" (represented as +inf.0) in a way
that is foreign to mathematics and only tangentially related to
its mathematical meaning.
It is sensible in terms of programming language semantics. But
someone who knew only traditional mathematical semantics would
have no way to guess the programming language semantics, and
would find them opaque.
Bear
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