My experience (bachelor's in math and physics, but I went into physics) is that if you want to be clear about including zero or not you add a subscript or superscript to specify. For non-negative integers you add a subscript zero (ℕ_0). For strictly positive natural numbers you can either do ℕ_1 or ℕ^+.

I hate those guys. I had that one prof at uni and he reinvented every possible symbol and everything was so different. It was a pita to learn from external material.

they’ll probably make up their own symbology just because it’s slightly more convenient for their proof

I feel so thoroughly called out RN. 😂

From what i understand, you can pay iso to standardise anything. So it's only useful for interoperability.

Yeah dont do that.

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.

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.

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.

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.