Axioms for Rational Numbers 9/14-9/15. Natural Numbers – Numbers used for counting: 1, 2, 3, and so on. Whole Numbers – Natural numbers and zero: 0, 1,

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Presentation transcript:

Axioms for Rational Numbers 9/14-9/15

Natural Numbers – Numbers used for counting: 1, 2, 3, and so on. Whole Numbers – Natural numbers and zero: 0, 1, 2, 3, and so on. Rational Numbers – Any number that can be expressed as the ratio of two integers, Integers – The numbers in the set

The Commutative Properties Addition: a + b = b + a Multiplication: ab = ba

The Associative Properties Addition: a + (b + c) = (a + b) + c Multiplication: a(bc) = (ab)c

The Identity Properties Addition: a + 0 = a Multiplication:

The Inverse Properties Addition: For each a, there is an additive inverse, -a, such that a + (-a) = 0 Multiplication: For each a (a does not equal 0), there is a multiplicative inverse,, such that

The Distributive Property of Multiplication over Addition a(b + c) = ab + ac