Cantor's Theorem

Cantor's theorem states that not all infinities are equal; specifically, the set of all real numbers is "more infinite" than the set of all natural numbers. This means you can't list all real numbers in a complete sequence like you can with natural numbers. In more intuitive terms, there are more ways to arrange or choose numbers than can be counted, indicating that some infinite sets are larger than others. This concept challenges our understanding of size and infinity, showing that not all collections of objects can be fully matched or paired.