1. Suppose the the setNof natural numbers is less than or equimunerous toA. 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.

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- April 12th 2007, 04:11 PMtaypezSet 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. - April 12th 2007, 05:11 PMPlato
Your #1 really depends upon the definition of 'infinite' your text uses.

For #2 read my pdf-file. - April 12th 2007, 06:21 PMtaypezSet Theory
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.