Set Theory

1. Suppose the the set N of natural numbers is less than or equimunerous to A. Show that A is infinite.

2. Prove by exhibiting an appropriate bijection that
C^AXB is equinumerous to (C^B)^A.

Thanks for any help.

Your #1 really depends upon the definition of 'infinite' your text uses.
For #2 read my pdf-file.

1. 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.

2. Prove by exhibiting an appropriate bijection that
C^AXB is equinumerous to (C^B)^A.

Thanks for any help.