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 0b = , then 0a a-= is the distance from 0 to a . Watch negative signs closely;
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This note was uploaded on 01/17/2012 for the course MATH V04 taught by Professor Michaelbowen during the Spring '12 term at Ventura College.