Is zero a natural number? Why or why not?

>>16712714 (OP)
Colloquially, zero is a natural number.

For the sake of mathematics, N usually does not include zero since it makes things easier to write out. N+ denotes N with zero.

>>16712714 (OP)
By default 0 isn't in N. Almost all the most legendary and canonical series and products run from 1, with binomials being the only real exception to the rule.

>>16712714 (OP)
>>16712760
Also enjoy these cats, which match your butterfly collar.

>>16712769
hello chatgpt

>>16712714 (OP)
There are several ways to think about this, so this is largely arbitrary. Take your pick.

The axiom of infinity in ZF gives the precise definition of the natural numbers as a set.
[eqn]\exists\mathbb{N}:\varnothing\in\mathbb{N}\land\forall{n}\left(n\in\mathbb{N}\implies n\cup\{n\}\in\mathbb{N}\right)[/eqn]
As you can see from the recursive definition, you need the empty set there as the first element in the recursion. You could take any other set, but then not all natural numbers correspond to finite cardinals.

If you want algebraic flavor to it, then the natural numbers can be defined as either a semigroup or a monoid under addition. The way you would canonically construct these is as free objects generated by the singleton set. This is more of a category-theoretic construction. If you choose it to be a semigroup, then zero isn't included. But then you're missing out on neat category-theoretic properties since composition in categories acts like a monoid.

>>16713028
type theorists need to touch grass

>>16712714 (OP)
You can't have zero of something in reality so no. You just don't have it.

>>16712714 (OP)
yes, because you're a virgin

>>16713156
I'd rather the trannies never go outside.

>>16712714 (OP)
Nothing is natural. Nothing is real. I wish nothing was imaginary, but everyone agrees it's too complex.

>>16713156
>answer OP’s question in a proper detailed fashion
>dude touch grass
fuck you

>>16712714 (OP)
yeah, how many notches does a counting stick have before it has one notch?, and if you argue that having no notches doesn't count as zero being a part of the counting stick's counting methodology, then what in the hell would one say that a counting stick without any notch counts as a counting stick?

>>16714156
It's not nice to make people think they're having a stroke

>>16713565
you are cheeky

>>16714173
you know, you ain't the first to tel me that my writing style makes them feel so...