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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 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 invented the concept of cardinality and ordered pairs, and proved that some infinities are larger than 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]].

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]].