integrity

You realize, of course, that my daffynition was never intended to open such a can of worms...

I have to question the integrity of a definition which falsely ascribes to the integers the requirement that they be greater than zero. Morality has nothing to do with it; the facts are as seanahan has said; the natural numbers are the positive whole numbers (sometimes called the counting numbers). The integers correspond to all whole numbers, negative or positive, and zero, by definition. Whimsy is all well and good, but not applied to such basic mathematical ideas as the integers.

(end of harrumphing diatribe)
Added on edit; I'm a little confused though, because Merriam Webster doesn't have anything about positive numbers in the definition of integrity. For integer it has
"any of the natural numbers, the negatives of these numbers, or zero".

Not being a mathematical type, I will maintain that any number identified as negative cannot be a number of integrity. It's a morals thing. There's nothing "natural" about miscreants like that.

Weird, because integer means any whole number, positive or negative or zero. Using natural implies any positive whole number. I question the validity of this MW definition.

The virtue of being a positive whole number, or zero.