Cantor–Bernstein–Schroeder theorem

The Cantor–Bernstein–Schroeder theorem states that if there are ways to match each element of set A with a unique element of set B, and also vice versa, then the two sets are essentially the same size, or have the same number of elements. In simpler terms, if you can pair every item in set A to an item in set B without leftovers, and also do the reverse, then there is a perfect one-to-one correspondence between them. This confirms that sets with these matching properties are 'equipotent,' meaning they can be considered to have equal cardinality.