P-1 The Real Number System

Real Numbers— Irrational Numbers— the real number that can not be written as the ratio of two integers. Rational Numbers— the real number that can be written as the ration p/q. They either terminate or repeat a sequence of digits indefinitely Non-integer fractions the (positive & negative) Integers—# line -3, , 0, 1, 2, 3, Whole numbers 0, 1, 2, 3, Negative Integers -3, , Natural Numbers 1, 2, 3 Zero

Number Lines 0 -Origin Negative Numbers Positive Numbers Coordinates

Absolute Value The magnitude of a number or distance from zero (disregarding the sign) |a| = { a if a  0 -a if a ≤ 0 Properties |a|  0|-a| = |a||ab| = |a| |b| a = |a| b |b| Distance on a number line |b-a| = |a-b|

Interpreting Inequalities, , ≤ Describe x ≤ 2 -2 ≤ x < 3 Inequalities can be used to describe subsets of Real numbers called intervals.

Algebraic Expressions 5x, 2x – 3, 4/(x 2 + 2) –Collection of variables and constants using +, - *, ÷ –Variable terms –Constants –Coefficients –Evaluate

Bounded Intervals Have endpoints; finite length NotationTypeInequalityGraph [a,b] (a, b) [a, b) (a, b] Closed Open Half a ≤ x ≤ b a < x< b a ≤ x < b a < x ≤ b a b [ ] a b ( ) a b ( ] a b [ )

Unbound Intervals Have infinite length NotationTypeInequalityGraph [a,∞) (a, ∞) (-∞, b] (-∞, b) Half Open Half Open x  a x > a x ≤ b x < b a b [ ( ) ] (-∞, ∞ ) Open -∞<x<∞