THE GATEBOOK

Normalization Lectures

Cantor's theorem shows that There is No surjective function from A to P(A). And There is No injective function from P(A) to A.

For finite sets, we can easily see that these are true because if |A| = n then |P(A)| = 2^n

So, There is No surjective function possible from A to P(A).

And There is No injective function from P(A) to A. https://www.whitman.edu/mathematics/higher_math_online/section04.10.html