Thread: Set Theory

Suppose the the set N of natural numbers is less than or equimunerous to A. Show that A is infinite. Infinite is defined as not having a bijection.

Originally Posted by taypez

Suppose the the set N of natural numbers is less than or equimunerous to A. Show that A is infinite. Infinite is defined as not having a bijection.

By definition if |N|<|A| the there is a injection from N to A.
Now, if there were a bijection from A to a finite subset of N then that leads to a contradiction. Therefore A must be infinite.