- Zorn’s lemma states that in a nonempty partially ordered set, if every chain has an upper
bound, there exists a maximal element, x in the partially ordered set. x is maximal, means
that if x ≺ y, it follows y = x. Show Zorn’s lemma is equivalent to the Hausdorff maximal
- Show that if Y, Y 1 are two Hamel bases of X, then there exists a one to one and onto map
from Y to Y 1. Thus any two Hamel bases are of the same size.