Theorem 7.2.5

##### Claim

Let $A$ be a set. The following statements about $A$ are equivalent.

- $A$ is infinite.
- $A$ contains a sequence of distinct terms.
- $A$ can be put into one-to-one correspondence with a proper subset of itself.

##### Proof

start typing proof here… Assume that A is an infinite set, that A contains a sequence of distinct terms, and that A can be put into a 1-1 correspondence with proper subset of itself.

$\square$

page revision: 6, last edited: 01 Dec 2009 20:02