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#### skatenerd

##### Active member

- Oct 3, 2012

- 114

"Every non-empty set of integers has a least element".

This seems pretty intuitively false, and so I tried to sum that up in the following way:

Suppose we have a subset \(A\) in the "universe" \(X\).

Let \(A=\{-n: n\in{N}\}\), a non-empty set ( \(N\) denotes the set of all natural numbers).

So \(A=\{-1, -2, -3, ..., -n\}\).

It is evident that there is no limit to how low the elements in \(A\) can become.

Since \(A\) is a non-empty set with no least element, we have arrived at the desired conclusion. Q.E.D.

My professor gave me one out of three points on this problem and I just can't figure out why...