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ARITHMETICS
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- The completeness of the propositional calculus was proved by Paul Bernays in 1918 and Emil Post in 1921, while the completeness of (first order) predicate calculus was proved by Kurt Gödel in 1930, and consistency proofs for arithmetics restricted with respect to the induction axiom schema were proved by Ackermann (1924), von Neumann (1927) and Herbrand (1931).
- Nevertheless, the main concern of the algebraists was to solve in terms of radicals, that is to express the solutions by a formula which is built with the four operations of arithmetics and with nth roots.
- The curriculum consisted of two major stages, including elementary stage (grammar, arithmetics, geography, history, languages, dogmatism or theology) and highest stage (theory of poetry, rhetorics, philosophy, theology).
- In computer arithmetics, the term coefficient (floating point number) is also sometimes used as a synonym for mantissa or significand.
- It taught the trivium (grammar, rhetorics, dialectics) as well as the quadrivium (arithmetics, geometry, music and astronomy).
- If k and l are multiplicatively dependent, then the Büchi arithmetics of base k and l have the same expressivity.
- Possibility of parallelizing heavy computations: parallelization is implemented for basic tensor calculus (arithmetics, contractions) and for calculus regarding affine connections (connection coefficients, action on a tensor field, Riemann curvature tensor).
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