Georg+Cantor



**Georg Ferdinand Ludwig Philipp Cantor ** (March 3, 1845 – January 6, 1918)

 *He discovered transfinite arithmetic  *He showed that there is not a single infinity, but an infinite hierarchy of infinities.  *He showed that the infinity of the integers is the same as the infinity of the rational numbers, but that the infinity of the real numbers is greater.  *He showed that the infinity of the power set is always greater than the original set, thus showing that there is no greatest infinity.  *He suffered from insanity but still managed to do brilliant, ground-breaking work.  *His diagonalization argument is one of the most fruitful ideas in mathematics. It was used to show that the halting problem is unsolvable and that no finite set of axioms will ever capture all of mathematics.  *He discovered the Cantor Set, another useful idea in topology