Math 3000 Lecture 15

Equivalent Sets

A ~ B iff there exists a bijection f: A B.

Almost an equivalence relation:

The equivalence classes under this relation are called cardinalities.

Finite Sets:

A is finite iff A = or A ~ k for some k in .

A set is infinite iff it is not finite.

is infinite.

A set is denumerable iff A ~ .

If A is denumerable and x A then A {x} is denumerable.

If A and B are disjoint denumerable sets then A B is denumerable.

is denumerable.

is denumerable.

is not denumerable (i.e. (0,1) is not denumerable).