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