Real Analysis - Cardinal Number, Finite Sets, Countable Sets

- Let f be a one-to one function from A into B with B finite. Show that A is finite.
- If A and B are finite sets, show that A union B is a finite set. Conclude that the finite union of finite sets is finite.
- Let f be a one-to-one function from A into B with B countable. Show that A is countable.
- If X is an infinite set and x is in X, show that X and X-{x} have same cardinal number.
- For a positive integer m, show that the set N of natural integers and the set N-{1,2,...,m} have same cardinal number.