- #1

happybear

- 19

- 0

## Homework Statement

If S is a set of function from {2,5} to a set of natural numbers, show S is countable?

The question also ask what if S is from a set of natural number to {2,5}, is that countable

## Homework Equations

## The Attempt at a Solution

I try to do it like this. Suppose E={2,5}, F be the set of natural numbers. suppose there are n natural numbers there. then

f(2)={n elements}. f(5) = elements, so there are n^2 elements of the function. So S is countable? It that right that I just assume there are n elements in the natural set?