mac1147_lecture1_2_b - L1 Real Numbers Algebra Review Sets...

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1 L1 Real Numbers; Algebra Review Sets of Numbers Natural numbers : Whole numbers : Integers : Rational numbers : { a x x b = , where a and b are integers and } 0 b Note : 1) Any integer m can be written as 1 m , thus, all integers are rational numbers. 2) Rational numbers include repeating and terminating decimals, for example: 1 0.333... 0.3 3 = = 0.9 1.0 1 = = Irrational numbers : Includes any real number that is not a rational number, for example: Real numbers : The rational and irrational numbers together. 2 Operations on the Set of Real Numbers Addition: a b + Multiplication: ab Properties of Real Numbers Commutative Properties : Associative Properties : Identity Properties : There is a unique number 0 , called additive identity , such that There is a unique number 1 , called multiplicative identity , such that Inverse Properties : There is a unique number b , additive inverse or negative of b , such that Subtraction : a b = For 0 b , there is a unique number 1/ b , multiplicative inverse or reciprocal of b , such that Division : ( 0 b ) / a b =
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