Let M be a set and A a subset of M with "=>" a preorder on M and "=>" on A a
weak order=> A is a chain on M.
A chain is maximal if there does not exist C' superset C s.t. C' is a chain on
M.
An upperbound of A subset of M <=> There exists m in M s.t. m"=>"a forall a in
A.
HausDorff's Maximal principle:
axiom of choice => every chain in a preordered set is contained in a maximal chain.
Zorn's Lemma: all chains in a preordered set have an upper bound => M has a
maximal element.