Suppose that gA B is a onetoone function If B is nite then A

Suppose that g:A B is a one-to-one function. If B is nite, then A is nite.

Provide complete and clear proof.

Solution

Here rule is that a 1-1 function is one in which each and every element of its domain is associated with one and only one (exactly one) element of its codomain. That means the cardinality of both the sets A and B will be equal to each other.

Or if g is 1-1, then card (A ) = card (B)

and thus if B is finite that means its cardinality exists and the same cardinality will be of set A also that means set A will also be finite.

Proved.