Georg Cantor (1845 – 1918) was a mathematician who invented set theory and proved that the set of real numbers is larger than the set of natural numbers. Thus implying that there exist infinite sets of different sizes (there is more than one infinity). In addition, he defined the cardinal and ordinal numbers and their arithmetic. His diagonal argument is fundamental in the solution of the Halting Problem and the proof of Gödel's first incompleteness theorem.
Source: Georg Cantor. (n.d.). Retrieved December 18, 2014, from http://en.wikipedia.org/wiki/Georg_Cantor
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