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- Axiom (Encarta Encyclopedia 2000) - Robert M. Baird; Microsoft Encarta Online
Axiom, in logic and mathematics, a basic principle that is assumed to be true without proof. The use of axioms in mathematics stems from the ancient Greeks, most probably during the 5th century BC, and represents the beginnings of pure mathematics as
- Gödel's Incompleteness Theorem - William Denton
Excerpts/quotes explaining Gödel's Incompleteness Theorem: any logical system contains a true statement that cannot be proven using that system's rules.
- Mathematics - John Savard
A collection of essays and illustrations: pentagonal tilings, infinity (Cantor's theory of transfinite numbers), rotations of the dodecahedron, Archimedean solids, the fourth dimension (regular polytopes), Gödel's proof and the halting problem, and
- Set Theory - Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to set theory. Naive set theory considers elementary properties of the union and intersection operators - Venn diagrams, the DeMorgan laws, elementary counting techniques such as the inclusion-exclusion
- Studies In Mathematics: Web Discussion - Breindel, Clair; University of Chicago
The University of Chicago's alternative course to calculus. The first quarter is number theory, and the second quarter is geometry and symmetry. When Bryan Clair taught the courses, he covered the history of number systems, different base number systems
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