well-ordering principle implies axiom of choice
Let be a collection of nonempty sets. Then is a set. By the well-ordering principle, is well-ordered under some relation . Since each is a nonempty subset of , each has a least member with respect to the relation .
Define by . Then is a choice function. Hence, the axiom of choice holds. ∎
|Title||well-ordering principle implies axiom of choice|
|Date of creation||2013-03-22 16:07:46|
|Last modified on||2013-03-22 16:07:46|
|Last modified by||Wkbj79 (1863)|