this post was submitted on 07 May 2024
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[–] kogasa 9 points 6 months ago* (last edited 6 months ago) (4 children)

Ehh, among American academic mathematicians, including 0 is the fringe position. It's not a "debate," it's just a different convention. There are numerous ISO standards which would be highly unusual in American academia.

FWIW I was taught that the inclusion of 0 is a French tradition.

[–] [email protected] 7 points 6 months ago* (last edited 6 months ago) (1 children)

I'm an American mathematician, and I've never experienced a situation where 0 being an element of the Naturals was called out. It's less ubiquitous than I'd like it to be, but at worst they're considered equally viable conventions of notation or else undecided.

I've always used N to indicate the naturals including 0, and that's what was taught to me in my foundations class.

[–] kogasa 1 points 6 months ago (1 children)

Of course they're considered equally viable conventions, it's just that one is prevalent among Americans and the other isn't.

[–] [email protected] 2 points 6 months ago (1 children)

I think you're using a fringe definition of the word "fringe".

[–] kogasa 1 points 6 months ago
[–] [email protected] 6 points 6 months ago

The US is one of 3 countries on the planet that still stubbornly primarily uses imperial units. "The US doesn't do it that way" isn't a great argument for not adopting a standard.

[–] [email protected] 3 points 6 months ago (1 children)

This isn't strictly true. I went to school for math in America, and I don't think I've ever encountered a zero-exclusive definition of the natural numbers.

[–] kogasa -1 points 6 months ago
[–] [email protected] 3 points 6 months ago (1 children)

I have yet to meet a single logician, american or otherwise, who would use the definition without 0.

That said, it seems to depend on the field. I think I've had this discussion with a friend working in analysis.

[–] kogasa 2 points 6 months ago (1 children)

I did say mathematician, not logician.

[–] [email protected] 3 points 6 months ago* (last edited 6 months ago) (1 children)

Logicians are mathematicians. Well, most of them are.

[–] kogasa 3 points 6 months ago (1 children)

But not all mathematicians are logicians.

[–] [email protected] 1 points 6 months ago