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

[Clément Pit-Claudel]

Hey Alan,


On 2018-08-31 15:59, Alan Mackenzie wrote:
> I'm speaking not as a mathematician, but as somebody with a degree in
> maths.

I'm speaking as someone who didn't expect a conversation like this one to spark 
such a strong-worded discussion :)  The whole debate rings odd to me (I agree 
with https://math.stackexchange.com/questions/36289/is-infinity-a-number: It 
comes down to the definition of "number," as well as the definition of 
"infinity")

> +/-infinity are not numbers.  They do not satisfy the axioms which
> define numbers.  For example they do not satisfy
> 
>     (x + y) + z = x + (y + z)
> 
> .  They cannot be made to satisfy these axioms.

I see the point, but… floating point numbers are not associative either, and it 
doesn't seem to controversial to call them "numbers".

>> 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.
> 
> That's a strawman.  The issue being discussed here is numbers, not
> arbitrary algebraic structures.

I read this as an example of the many meanings that the word "number" can take, 
depending on the context.  It sounded pretty convincing.

>> .... she has no exclusive claim over the definition (such as it is) of
>> "number"
> 
> That's analagous to saying that climate scientists don't have the
> exclusive say-so about climate change.  Ha ha, who needs experts?

This is a very strongly worded charge.  The original formulation could have 
been better, but to me it didn't look like a rejection of expertise… rather, I 
took it as a statement that the word "number" gets assigned different meanings 
across fields.

>> (and I'm a bit surprised if she hadn't heard of at least one of the
>> extended real lines I linked).
> 
> Again, offensive.  "Infinity", with or without a sign, might be classed
> as an "extended number", but as noted above, is not a number.

I don't understand this part.  Does the word "number" on its own even have a 
strict definition, beyond something vague like Wikipedia's "mathematical object 
used to count, measure and also label"?

Cheers,
Clément.