/sci/ - Science & Math

Pick a random real number, assign it to 1. Pick another random real number, assign it to 2. Repeat the process to infinity until all real numbers have been mapped. Since the natural numbers are infinite, there is no point at which a real number cannot be mapped to a natural number.

Therefore there exists a bijection between the reals and natural numbers, and between all infinite sets. So all infinite sets have the same cardinality.

Q.E.D.