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

From: Pip Cet
Subject: Re: Making 'eq' == 'eql' in bignum branch
Date: Wed, 29 Aug 2018 13:15:27 +0000

On Wed, Aug 29, 2018 at 3:42 AM Herring, Davis <address@hidden> wrote:
> > Signed infinities are convenient symbols, but they're not numbers; I
> > recall the horrified reaction of a mathematician when I told her about
> > IEEE infinities (she thought I was making it up about NaNs).
> Of course +/-inf are numbers.

I'm sorry I made a tangential mathematical statement; while I think
it's correct that the usual definition of "number" excludes infinities
(but not numbers that happen to be infinite), you are perfectly
correct that it's okay to redefine the term as you see fit. To get
this back to Emacs matters, `numberp' is fine as it is.

> They're not real numbers, but neither are complex numbers, split-complex 
> numbers, dual numbers, p-adic numbers, quaternions, octonions, sedenions, 
> hyperreal numbers, or (please no) surreal numbers.  With all due respect to 
> your mathematician friend, she has no exclusive claim over the definition 
> (such as it is) of "number" (and I'm a bit surprised if she hadn't heard of 
> at least one of the extended real lines I linked).

She has; she simply has a different definition of "number" (and no
doubt the three of us have three different definitions of the term).

> NaN, on the other hand, is of course a floating-point value that explicitly 
> claims not to be a number.  I'm not sure whether to believe it; it seems very 
> useful that the operations on floating-point "numbers" are closed, but that 
> depends on NaN being one of them...

Four definitions!

For those not familiar with APL, JavaScript is a popular language that
has Math.min() = Infinity.

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