Re: Making 'eq' == 'eql' in bignum branch

[Herring, Davis]

> Because this is an emacs groups, and we have to use "number" in that
> context.

I think we've finally found the root of our miscommunication: I took the 
discussion to be about numbers in general, from which we might draw useful 
conclusions for Emacs, rather than to (already) be about Emacs' model for the 
real numbers.

>> What is the list of such axioms?
> 
> Obviously different for different sorts of number.

Certainly: that was the entire point of my most recent message -- and of my 
first in this thread.

> For the real numbers, [...]

...And conversely I was never asking for the axioms for real numbers, although 
it's good to remember those every once in a while (I usually think only of 
Cauchy completeness, but that allows interlopers like the Levi-Civita field).

> Note that these two "infinities" are being proposed as members of
> (Emacs's) real numbers, so it is reasonable to focus on real numbers.

They're not being proposed -- they're already there (if not in C, then at least 
on all machines in common use), since IEEE 754 is in fact based on the 
(affinely) extended reals.  It's begging the question to call Emacs' numbers 
real and then object to the inclusion of infinities based on that, but you're 
right that it's reasonable to _focus_ on the cofinite real subset when trying 
to engineer a usable system we can reason about.

Davis