He lived 1781 to 1848 and studied continuity and set theory. Real numbers in closed intervals can be in one-to-one correspondence with real numbers in other closed intervals. Infinite sequences in closed intervals have limits {Bolzano-Weierstrass theorem}. Truths can be a priori. Logic is about ideals, not about time or space.
He lived 1834 to 1923 and invented Venn diagrams.
He lived 1845 to 1918 and studied set theory, infinity, continuity, transfinite numbers, union, intersection, conjunction, disjunction, bound, extension principle, abstraction principle, and one-to-one correspondence.
He invented continuum hypothesis. Cardinal-number series and ordinal-number series are infinite. Irrational numbers in closed intervals are rational-number-series limits. Sets of limits can have sets of limits, and so on, to infinity.
Geometrical-figure or space topologies are points related by distance functions or limits. For any real number n, 2^n > n.
He lived 1861 to 1931. Ordinal numbers are well-ordered by definition. Ordinal-number sets must then have a greatest ordinal number. However, the set can be infinite and not have greatest ordinal number. Therefore, infinite ordinal-number sets cannot exist {Burali-Forti paradox}. Ordinal-number sets are higher-ordinal-number-set subsets.
He lived 1871 to 1956 and invented Zermelo-Fraenkel set theory [1904 to 1908]. Infinite sets can contain sets with no elements in common. Methods to choose one element from each set must exist {axiom of choice, Zermelo}. If sets have no defined choice function, sets must use axiom of choice.
He lived 1868 to 1942, invented generalized continuum hypothesis [1907], and invented Hausdorff space.
He lived 1891 to 1965 and improved Zermelo-Fraenkel set theory [1922].
He lived 1934 to ? and proved that continuum hypothesis was indeterminable under set theory [1963].
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Date Modified: 2022.0225