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Georg Cantor

The founder of the set theory. Born in St. Petersberg, Russia, and studied in Germany. His studies on the nature of "infinity" enabled us to treat this abstruse concept with mathematical precision.

Cantor discovered an ingenious argument for proving that there are more real numbers than natural numbers (the cadinaliy is greater with the former than with the latter); since this argument makes use of a two dimensional table of infinie elements and the elements on the diagonal line (from left top to right bottom) are crucial, this is called "diagonal argument", and it became an indispensable method for logicians's proof. For instance, Goedel's incompleteness makes an essential use of it for cnstructing an "undecidable proposition".


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Last modified Dec. 3, 2008. (c) Soshichi Uchii