Austin Hastings <[EMAIL PROTECTED]> writes:
> Half of all numbers in [0, Inf) are in the range [Inf/2, Inf). Which
> collapses to the range [Inf, Inf).
It's not that simple. By that reasoning, 10% of all numbers in
[0,Inf) would be in [Inf/10,Inf), also reducing to the range
[Inf,Inf). For that matter, 99% of them would be in [Inf/100,Inf),
which would reduce to [Inf,Inf). But you can't do that kind of
arithmetic with Inf. You're trying to pretend you're working with a
natural number or a specific real, when in fact it's a cardinality (or
a class of cardinalities, or an infinite set of cardinalities, or
something along those lines). If you want to do addition and
multiplication on Inf, you have to redefine addition and
multiplication to get away from the CPU's finite arithmetic, and you'd
also need to treat Inf more completely than Perl does. (Perl treats
all infinities as the same, which is (mathematically speaking)
patently rediculous, because for practical purposes it never matters
to most software, and if somebody wants to clone Mathematica they'll
be writing their own math library anyway.)
It would be *nice* to have this stuff properly supported in a
programming language, sure, but it would also be a ton of work and can
probably wait for at least Perl7.
Oh, and the hardware available to most folks isn't up to the challenge
of picking a properly random number between 0 and Inf yet, either.
Most of the time it wouldn't fit in RAM. Predicting when this
challenge will be overcome is left as an exercise to the reader.
--
$;=sub{$/};@;=map{my($a,$b)=($_,$;);$;=sub{$a.$b->()}}
split//,"[EMAIL PROTECTED]/ --";$\=$ ;-> ();print$/
