Show that a subset of a countable set is also countable.

Step 1:

We have to prove that a subset of a countable set is also countable.

Step 2:

This statement can be proved by the theorem

Theorem: Every subset of a countable set is countable

Proof: Suppose x1 , x2, x3……… is a countable set A and B is any non-empty subset of A

If , for n, the element of xn belongs to B.

For each n

Let k(n) denote the number of elements x1,, x2, x3…….xn which belong to the subset of B.

Then 0where B is countable