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22 Cards in this Set

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 Closure Axiom of Addition CLAA If a+b=c, then c is a real number Closure Axiom of Multiplication ClAM If ab=c, then c is a real number Commutative Axiom of Addition CAA a+b=b+a Commutative Axiom of Multiplication CAM ab=ba Associative Axiom of Addition AAA (a+b)+c=a+(b+c) Associative Axiom of Multiplication AAM (ab)c=a(bc) Axiom of Zero for Addition (Identity for Addition) A0A (Id+) a+0=0+a=a Axiom of One for Multiplication (Identity for Multiplication) A1M (Idx) ax1=1a=a Axiom of Additive Inverses AAI a+(-a)=-a+a=0 Axiom of Multiplicative Inverses AMI *A cannot equal 0* a x 1/a = 1/a x a =1 Distributive Axiom of Multiplication over Addition DAMA a(b+c)=ab+ac Reflexive Axiom a=a Symmetric Axiom If a=b, then b=a Transitive Axiom If a=b and b=c, then a=c Definition of Subtraction a-b=a+(-b) Definition of Division a(division symbol)b or a/b = a x 1/b Binary Operation A rule for combining two real numbers (or things) to get a unique (one and only one!) real number (or thing) upside down A means "for all, for each, for every, for any..." universal quantifier backwards E means "there exists for at least one, for some..." backwards E with ! means "there is exactly one x, or a unique x" straight vertical line means "such that" Ring system in math with these axioms is called a ring