Cantor-Bernstein-Schröder theorem

The Cantor-Bernstein-Schröder theorem states that if two sets can each be mapped into the other without losing any elements (meaning each has an injective function into the other), then the two sets have the same size or cardinality. In simpler terms, if you can find a way to match every element of set A to a unique element of set B, and vice versa, then there is a perfect one-to-one correspondence between all elements of both sets, proving they are essentially the same size, even if they are infinite.