Template:AotD
Zorn's Lemma
Zorn's Lemma is a set theoretic result which is equivalent to the Axiom of Choice.
Let
be a partially ordered set.
We say that
is inductively ordered if every totally ordered subset
of
has an upper bound, i.e., an element
such that for all
,
. We say that
is strictly inductively ordered if every totally ordered subset
of
has a least upper bound, i.e., an upper bound
so that if
is an upper bound of
, then
.
An element
is maximal if the relation
implies
. (Note that a set may have several maximal... [more]