Question

can someone explain Zorn's theorem and how it is equivalent to the axiom of choice.

Answer 1

http://www.math.grinnell.edu/~miletijo/museum/choice.html

Answer 2

That was good stuff but it drought talk about the relation to zorn's

Answer 3

Didn't *

Answer 4

Zorn's lemma, also known as the Kuratowski–Zorn lemma, is a proposition of set theory that states: Suppose a partially ordered set has the property that every chain (i.e. totally ordered subset) has an upper bound. Then the set contains at least one maximal element.

The terms are defined as follows. Suppose (P,≤) is a partially ordered set. A subset T is totally ordered if for any s, t in T we have s ≤ t or t ≤ s. Such a set T has an upper bound u in P if t ≤ u for all t in 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 in P such that for no element x in P, m < x.

Answer 5

I can google @futuremathprofessor....I need to understand how it is equivalent to the axiom of choice.