The Well-Ordering property states that every nonempty set of positive integers has a least element.

This is common sense, but what if you were told to prove that every nonempty set of negative integers has a greatest element.

Is this a suitable proof?:

The statement that every nonempty set of negative integers has a greatest element is true because we can say what that element is. -1 is the greatest negative integer in the set of all positive integers.

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Sorry, I'm new to this site and I don't know how to ask a follow up question and have it known that there is a follow up question.

Reply to first response:

The well ordering principal works because the set of all positive integers, an infinite set, has a least element.

Can we use the fact that the set of all negative integers, an infinite set, has a greatest element as proof that every subset of the set of all negative integers must then have a greatest element?