Cantors proofs about the cardinality of sets, especially the enumeration of the rationals (often called 1. diagonal argument here) and his proof of the existanc

Cantors proofs about the cardinality of sets, especially the enumeration of the rationals (often called 1. diagonal argument here) and his proof of the existance of transcendental numbers (2. diagonal argument) are among my favorite pieces of maths ever. So easy to understand but still mind-expanding, and pretty independent of algebra etc