Definition
In 1936, Alfred Tarski gave an axiomatization of the real numbers and their arithmetic, consisting of only the eight axioms shown below and a mere four primitive notions: the set of reals denoted R, a binary relation over R, denoted by infix <, a binary operation of addition over R, denoted by infix +, and the constant 1.
Related concepts
0.999...Abelian groupAbsolute differenceAlfred TarskiArchimedean groupAssociativityAsymmetric relationAxiomAxiomatizationBinary operationBinary relationCantor setCantor–Dedekind axiomCommutativityCompleteness of the real numbersConstruction of the real numbersContrapositiveDecidability of first-order theories of the real numbersDedekind-completeDivisible groupExtended real number lineFirst-order logicGregory numberInfixIrrational numberLinearly ordered groupNormal numberOrdered fieldPrimitive notionRational numberRational zeta seriesReal closed fieldReal coordinate spaceReal lineReal numberReflexive relationSecond-order logicSet (mathematics)SubsetTotal orderingVitali set
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