Explain w by the set A is countable if and only if |A| ≤ |Z+|.

We need to show that a set A is countable if and only if

Step 1</p>

By definition, A set is called countable if it is finite or it has the same cardinality as the set of positive integers.

Step 2</p>

By definition of cardinality , if there is injection (one to one relation) from A to B then the cardinality of A is less than or equal to the cardinality of B.

Therefore we can write it as

Step 3</p>

There is a proposition stating that if be an injection .then if B is countable then A is also countable.