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DEDEKINDS INVENTION OF IDEALS
THE DISCOVERY OF NONEUCLIDEAN GEOMETRY
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algebraic analysis appeared applied approach attempt axiom Berlin Bieberbach Brouwer calculating called century closed complete concept connection considered consistency construction contained continuous correspondence course curve Dedekind defined described determined differential equations dimension discussed domain early edited example existence expressed fact field finite first-order logic formal formula foundations Frege functions fundamental Gauss gave geometry German given Hilbert History ideal ideas important infinite Institute interest invariance Journal Killing later lecture letter linear linear system lines machine manifold mapping mathematicians mathematics Mathematik means methods natural Neumann non-Euclidean geometry notion objects physical plane position possible present problem proof properties proposition proved publication published quantifiers question second-order separation set theory showed solution solve space sphere surface symbols theorem theory tion topology transformation Turing Turing's types University variables Volume