The first definition of well-ordering given on Proofwiki.org is:
Let (S,⪯) be an ordered set.
Then the ordering ⪯ is a well-ordering on S iff every non-empty subset of S has a smallest element under ⪯:
But the formal statement here doesn't seem right. Where is the condition that
T must be non-empty? I thought there should be something between
∀T⊆S and the rest, e.g.
Is the original statement wrong, or am I missing something?