[Koshkin]

Indeed, polynomials, for instance, start with a power of zero. At the same time, there is a reason why the natural numbers begin with 1, and, in practical terms, there is a certain convenience in the count (size) being the same as the last index.

[ogogmad]

The natural numbers don't start with 1... The convention is inconsistent, but for many mathematicians, especially including logicians, they start with 0. It is best not to use the term "natural numbers" at all.

By the way, your point about polynomials works in favour of the convention that 0 is a natural number.

[Koshkin]

Try thinking of being the zeroth person in a line. Or your child being in the zeroth year of her life.

[ogogmad]

How many lions are in my room at the moment? Hopefully zero.

[Koshkin]

But zero sheep is not a flock.

(Besides, there's uncountably many things you have zero of in you room.)

[ogogmad]

> But zero sheep is not a flock.

So one isn't a natural number?

> (Besides, there's uncountably many things you have zero of in you room.)

;) Exactly. Zero is the most natural number.

[Koshkin]

So, on your scale, which is the first natural number?