Is zero a natural number?

[polymath257]

Depends a bit on the book used.  One way of resolving ambiguities is as follows:

Positive: >0
Negative: <0
Non-negative: >=0
Non-positive: <=0

So, 0 is not negative, not positive, but is non-negative and non-positive.

Well that's just double talk. Don't even try to tell me about swamp land in Florida.

I suppose next you'll tell me that infinity exists between 0 and 1.

No, it is precision of language.

There are infinitely many rational numbers between 0 and 1. That is different than infinity being between them.

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Well that's just double talk. Don't even try to tell me about swamp land in Florida.

I suppose next you'll tell me that infinity exists between 0 and 1.

Between 0 and 1, there exists an infinitude of numbers, some of which are countable (the rational) and others that are not countable (the reals, complex and surreals).

I would caution: the numbers themselves are not countable or uncountable. The *sets* of those numbers are.

So, a set containing all numbers of the form a+b*sqrt(2) is a countable set even though it has irrational numbers in it.

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Really, we're going to have a debate over nothing? No thanks.

Edward Grant has a wonderful book about medieval notions of the vacuum called 'Much Ado About Nothing'. It's an interesting read. You might like it.

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What's the alternative?  That the laws of nature not be describable by some mathematical models?  The term for such a world would be "magic".

As for "nothing" no one has, to my satisfaction, ever provided any physical description of that.  To use "nothing" in a sentence is to give it meaning, if only as an abstraction.  One might as well ask what color Saturday is.

Well...it seems to me that nothingness literally means an absence of physicality.

Why just physicality?