Originally Posted by

**Plato** Maybe we should discuss this question in detail.

When I first read it, I dismissed it as some author’s effort to construct a question to get at a fundamental property of cardinality.

These are really matters of definitions.

If there is an injection from A to B, then the cardinality if A, $\displaystyle |A|\le |B|$.

Then if there is a surjection from B to A, then $\displaystyle |B|\ge |A|$.

In terms of this particular question, any subset of a countable set is countable.

**It just seems to me that this question almost answers itself.**