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addition and multiplication applied arithmetic assumed assumption axiom of choice axiomatic method binary operation Boolean algebra calculus of propositions called cardinal number circle commutative complex number concept congruent considered consistency construct contains corresponding deductive defined definition denote discourse dyadic relation elementary equal equation established Euclid's Elements Euclidean geometry Euclidean tools example exists Figure finite number following theorems formula function given Greek Hilbert hypothesis implied independent infinite integers interpretation intersect inverse line segment Lobachevskian logic mathematical induction mathematicians means natural number system non-Euclidean geometry ordered field ordered pairs parallel postulate perpendicular positive integers postulate set prime number primitive terms principle Problem projective geometry proof properties prove quadrilateral rational numbers real number system reductio ad absurdum right angles Section set of postulates set theory Show sides space sphere statements straight line subset symbols tautology transformation true truth table
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