Infinity is a crucial concept in mathematics, and there are different levels of infinity. Georg Cantor developed the theory of infinite sets, which compares the sizes of infinite sets and shows that there are many infinities. Two sets are the same size if we can make a one-to-one correspondence of their elements. Countably infinite sets are the baseline level of infinity, which includes the natural numbers. Cantor's ideas and theorems are the foundation of modern mathematics.