Is 0 a natural number?

I think that modern definitions include zero as a natural number. But sometimes, expecially in analysis courses, it could be more convenient to exclude it.

Pros of considering 0 not to be a natural number:

generally speaking 0 is not natural at all. It is special in so many respects;

people naturally start counting from 1;

the harmonic sequence 1/n is defined for any natural number n;

the 1st number is 1;

in making limits, 0 plays a role which is symmetric to ∞, and the latter is not a natural number.

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