Is this Zorn's lemma?

Question

Is this correct? I think it is wrong. According to wikipedia

Suppose a partially ordered set P has the property that every chain (i.e. totally ordered subset) has an upper bound in P. Then the set P contains at least one maximal element.

However, can't see how this is equivalent to the definition given in notes.

Answer 1

To understand the statement of the theorem you would have to look up what an inductive partial order is. If you do, you should find that it is a partial order in which every chain has an upper bound. Therefore the statements are the same. (I do not have access to your notes to know whether the meaning of inductive was made clear there.)

Answer 2

Yes, that is the statement of Zorn's Lemma. If S is a partially ordered set in which every chain has an upper bound (i.e. if S is an inductive set and is partially ordered) then S has a maximal element. Your notes say exactly what Wikipedia is saying.