Tukey's lemma
Encyclopedia
In mathematics, Tukey's lemma, named after John Tukey
, states that every nonempty collection of finite character has a maximal element
with respect to inclusion. It is equivalent to the Axiom of Choice.
John Tukey
John Wilder Tukey ForMemRS was an American statistician.- Biography :Tukey was born in New Bedford, Massachusetts in 1915, and obtained a B.A. in 1936 and M.Sc. in 1937, in chemistry, from Brown University, before moving to Princeton University where he received a Ph.D...
, states that every nonempty collection of finite character has a maximal element
Maximal element
In mathematics, especially in order theory, a maximal element of a subset S of some partially ordered set is an element of S that is not smaller than any other element in S. The term minimal element is defined dually...
with respect to inclusion. It is equivalent to the Axiom of Choice.