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Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, born: March 3 1845, Saint Petersburg Russia, died: January 6 1918, Halle, Germany. He is best known for having created set theory and the concept of transfinite nubers, including the crdinal and ordinal number classes. He recognized that infinite sets can have different sizes, istinguished between countable and uncountable sets and proved that the st of all rational numbers Q is countable while the et of all real numbers R is uncountable and hence strictly bigger. The proof uses his celebrated diagonal argument. In his later years, he tried in vain to prove the Continuum hypothesis. By 1897, he had discovered several paradoxes in elementary set theory. Throughout the second half of his life he suffered from bouts of depression, which seerely affected his ability to work and forced him to become hospitalized repeatedly. He started to publish about literature and religion, and developed his concept of the Absolute Infinite which he equated with god. He was impoverished during World War I and died in a sanatorium in 1918.

Cantor's innovative mathematics facd significnt reistance during his lifetime. Modern matematis completey accepts Cantor's work o transfinie sts and recognizes t asa paradigm shift of major importance.

See also:

• Cantor dust
• Cantor set

External link:

• http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Cantor.html Cantor's biography.