Cantor was the first to "put infinity on a firm logical foundation."<ref name="Cantor bio">http://scidiv.bellevuecollege.edu/Math/infinity.html</ref> His invention of set theory helped him achieve this extraordinary goal.<ref>http://www.engr.iupui.edu/~orr/webpages/cpt120/mathbios/gcant.htm</ref> He "described a way to do arithmetic with infinite quantities useful to mathematics."<ref name="Cantor bio"/>
Cantor invented the concept of cardinality and ordered pairs, and how some infinities are larger tan others.<ref>http://www.economicexpert.com/a/Cardinal:number.html</ref>
Cantor's best known proof is his technique of [[Diagonalization|Cantorian Diagonalization]], a method useful to prove that the [[real numbers]] are larger in [[cardinality]] than the [[integers]]. He is also known for his [[Cantor_set|Cantor Set]]<ref>http://mathworld.wolfram.com/CantorSet.html</ref> and [[Cantor Intersection Theorem]].