kogasa

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

I did say mathematician, not logician.

There can't really be an argument either way. It's just a matter of convention. "Natural" is just a name, it's not meant to imply that 1 is somehow more fundamental than -1, so arguing that 0 is "natural" is beside the point

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.

Limits at infinity are one thing, but infinite ordinals are meaningfully used in set theory and logic

The question doesn't make sense, there are many things which have an infinite quality (like infinite cardinality) or are called infinite/infinity (like infinite cardinals and ordinals). They're not contradictory. They coexist the same as all finite things do.

I dunno about proving you wrong, but the fact that you can comfortably say there is no largest natural number is kind of a belief in infinity

Holomorphicity is equivalent to (or defined as) being differentiable in a nonempty, connected, open set, so it's not asking much. Even then, functions which fail to be holomorphic can often be classified in a similarly rigid way.

At some level, the goal of customer service is to prevent customers from bothering your employees. A sufficiently confusing first level of customer service is just as good as one that actually attempts to help you because it convinces you to give up

That would make it impure

I'll take the stick and use it to make you give me the rock.

Monkey laundering.