Andrew Barnert writes:
> Well, there are an infinite number of ever larger infinite
> ordinals, ω or ω_0 being the first one, and likewise an infinite
> number of infinite cardinal, aleph_0 being the first one, and
> people rarely use the ∞ symbol for any of them.
s/people/mathematicians/ and I'd agree with you. But I did write
"people".
> There are a few different obvious ways you could build an
> IEEE-float-style complex out of IEEE floats, but the one that C99
> and C++ both use is probably the simplest: just model then as the
> Cartesian product of IEEE float with itself, applying the usual
> arithmetic rules over IEEE float.
FVO "simple" = "simplistic". :-)
> And that means these odd things make sense:
FVO of "sense" = "derived from an arbitrary model (as long as we're
consistent)". (This time I'm not trolling.)
> >>>> complex("inf")
> > (inf+0j)
> >
> > Oof. ;-)
>
> What else would you expect?
I don't "expect" anything when there are several competing
interpretations. I would *like* it to be 'complex("inf")' FVO inf =
projective complex plane infinity. My reasoning is the available
*mathematical* values we model should make sense as expressing the set
of possible limits in polar coordinates as well as in Cartesian
coordinates (and as the limits of arbitrary lines). But these are in
some sense distinct, with a couple of exceptions. So I would prefer
my calculations to tell me "you're out of bounds" rather than give me
a result that looks precise but actually doesn't tell me much about
the limiting process. E.g., the mathematical limit in R^2 of (ax, bx)
for all a, b > 0 is (inf, inf) -- thank you very much, I guess. By
contrast, +inf and -inf for R tells me a lot.
> Again, Python, C, and lots of other languages agree here, and it
> makes sense once you think about it. We have a number that’s either
> indeterminate or multivalued or unknown on one axis, but it’s
> infinite on the other axis, so whatever value(s) it may represent,
> they all must be infinite.
Pragmatically, that is what I said I like, except I like it in maximum
generality. ;-)
Steve
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