# Discrete Math “Well Order”

the definition of a well order is that if $R$ is a linear (order) and every non-empty subset of $A$ has a least element. I understand that

$(\mathbb N,\le)$ is a well-order but how come

$(I,\le)$ with subset of negative integers is not a well-order?

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With the positive integers, I could take any subset and find a least element. For example, if I take the set of all even positive integers, there is a least element: $2$. What if you take the set of all even negative integers? Is there a least one? (What if you take the whole set of negative integers; is there a least negative integer?) – Benjamin Dickman Nov 1 '12 at 5:40