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h_basic_algebra_review

h_basic_algebra_review - BASIC ALGEBRA REVIEW Assume that...

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VC DEPARTMENT OF MATHEMATICS REVISED SUMMER 2006 BASIC ALGEBRA REVIEW Assume that letters such as a , b , x , y represent real numbers, unless otherwise specified. I. Subsets of the real numbers: Integers include whole numbers and their negatives. The rationals include all integers AND all fractions, and have repeating decimals. Irrationals (e.g., π , 2 , etc .) include all other real numbers and have non-repeating decimals. A real number is either rational or irrational but not both. II. Order: a b < means that a is located to the left of b on the real number line; a b means that either a is to the left of b , or a and b coincide. 0 is greater than all negative numbers, and less than all positive numbers. III. Absolute value: a b - is the distance (on number line) from a to b , disregarding direction (so the result of an absolute value is always non-negative). If a b > , then a b a b - = - ; else ( ) a b a b b a - = - - = - . If 0 b = , then 0 a a - = is the distance from 0 to a . Watch negative signs closely; 3 3 - = but 3 3 - = - .
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