“Zorn’s Lemma stands for – Every non-empty partially ordered set in which every chain (i.e. totally ordered subset) has an upper bound contains at least one maximal element.
It is named after the mathematician Max Zorn.
The terms are defined as follows. Suppose (P,≤) is the partially ordered set. A subset T is totally ordered if for any s, t ∈ T we have either s ≤ t or t ≤ s. Such a set T has an upper bound u ∈ P if t ≤ u for all t ∈ T. Note that u is an element of P but need not be an element of T. A maximal element of P is an element m ∈ P such that the only element x ∈ P with m ≥ x is x = m itself. Read More »