[jmkr]

+1 for peano arithmetic club.

I never realized it was controversial. I think I've always included 0 in the nat numbers since learning to count.

But there are some programming books I've read, I want to say the Little Typer, or similar, that say "natural number" or "zero". Which makes actually confuses me.

[nivertech]

IMO zero represents an absence of quantity and doesn't appear in Nature, so it cannot be classified as a Natural number

Just like a negative numbers, it's a higher-level abstraction or a model, not a direct observation from the Nature

Likewise, the digit "0" originating from the Hindu-Arabic numeral system[1] is merely a notation, not a number

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1. https://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_s...

[feoren]

> zero represents an absence of quantity and doesn't appear in Nature

From one point of view, zero never appearing in nature is exactly an example of it appearing in nature!

From another point of view, do you not think a prairie dog has ever asked another prairie dog, "how many foxes are out there now?" with the other looking and replying "None! All clear!"? Crows can count to at least 5, and will count down until there are zero humans in a silo before returning to it. Zero influences animal behavior!

From a third point of view, humans are natural, so everything we do appears in nature.

From a fourth point of view, all models are wrong, but some models are useful. Is it more useful to put zero in the natural numbers or not? That is: if we exclude zero from the natural numbers, do we just force 90% of occurrences of the term to be "non-negative integers" instead?

[jmkr]

A symbol being arbitrary doesn't influence the reality of the meaning behind a thing. I've always thought about `zero` while counting, it never was about `0`.

I observe zero.

I don't think zero is an absence of quantity. I don't think zero is the null set.

You can write types in a programming language, but there are other type theory books that do include zero in the natural numbers. And type theory comes from number/set theory. So it's ok if you decide to exclude it, but this is just as arbitrary.

In fact I'd be happy to write `>=0` or `>0` or `=0` any day instead of mangling the idea of zero representing 0 and zero representing something like `None`, `null` or any other tag of that sort. I don't think the natural world has anything like "nothing" it just has logical fallacies.