# Is this Zorn's lemma?

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.

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Your confusion might come from the fact that you are thinking of a defintion of inductive set that is not meant in this context. You are probably thinking of sets that contain 0 and are closed under successors. Here inductive partially ordered set certainly means partial order in which every chain has an upper bound. – Stefan Geschke Dec 29 '11 at 11:29
-1 for not citing the source for the text you speak about. – Henning Makholm Dec 29 '11 at 23:07