11 Oct '04 15:471 edit

Let F(X) be the set of all finite subsets of X. For each of the following, either give an explicit example or show why it can't be done.

1. an injection from F(N) to N (counting numbers);

2. an injection from F(R) to R (real numbers).

(For those who don't know, an injection is a function f for which f(x) is different from f(y) whenever x is different from y.)

1. an injection from F(N) to N (counting numbers);

2. an injection from F(R) to R (real numbers).

(For those who don't know, an injection is a function f for which f(x) is different from f(y) whenever x is different from y.)