On 21/04/14 19:39, Bear wrote:
> 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.

Perhaps it is worth our wording around what "inexact numbers" means
explicitly referring to intervals, then?

>
> 		Bear
>

ABS

--
Alaric Snell-Pym
http://www.snell-pym.org.uk/alaric/

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