無限について

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Infinity presents special problems. From the time people began to think about the world they lived in, questions about infinity arose. But the interaction of infinity and mathematics is seldom revealed so clearly as in the study of the infinite among the ancient Greeks. Theses questions are very fundamental and must have troubled thinkers long before recorded history. An actual infinite set requires a measure, and we have to move forward to Cantor near the end of the 19th Century before a satisfactory measure for infinite sets was found. The approach based on measuring information suggests that an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.
神戸市立工業高等専門学校の論文
2007-03-01