5.5 Real Numbers and Their Properties

Objectives Recognize the subsets of the real numbers. Recognize the properties of real numbers.

Real Number Set

Example Given the following set: List the elements which are A.natural numbers B.whole numbers C.Integers D.rational numbers E.irrational numbers F.real numbers

Properties of Real Numbers NameMeaningExample CLOSURE property of addition If a and b are real numbers, then a + b is a real number COMMUTATIVE property of addition a + b = b + a ASSOCIATIVE property of addition (a + b) + c = a + (b + c) IDENTITY property of addition There is a number 0 such that a + 0 = a INVERSE property of addition For every a, there is –a such that a + (-a) = 0

Properties of Real Numbers NameMeaningExample CLOSURE property of multiplication If a and b are real numbers, then a· b is a real number COMMUTATIVE property of multiplication a· b = b· a ASSOCIATIVE property of multiplication (a · b) · c = a · (b · c) IDENTITY property of multiplication There is a number 1 such that a· 1 = a INVERSE property of multiplication For every a, a ≠ 0, there is 1/a such that a · 1/a = 1 DISTRIBUTIVE property of multipl. over addition a (b + c) = a· b + a· c

Example Which property is used? A) B) (4 + 7) + 6 = 4 + (7 + 6) C) D)

Example