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## Pre Calculus Sec 1.1 Real Numbers

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**Pre CalculusSec 1.1 Real Numbers**Objectives: To review the set of Real Numbers To review the properties of Algebra To understand interval and set notation.**Real Numbers**• Natural Numbers: 1,2,3,4,… • Integers: -,…-3,-2,-1,0,1,2,3,… • Rational Numbers: any # that can be written as a ratio of integers (as a fraction). • Irrational Numbers: any # that cannot be written as a fraction.**CLASS WORK**• Given the set, list the elements of the set that are: • Natural numbers • Integers • Rational numbers • Irrational numbers**Properties of Real Numbers**Commutative Property: a + b = b + a ab = ba order doesn’t matter Associative Property: (a+b)+c = a+(b+c) (ab)c = a(bc) order doesn’t change**Distributive Property:**a(b+c) = ab + ac you can add then multiply or multiply then add.**CLASS WORK**State the property of real numbers being used. 2. 3. 4.**Sets & Elements**• A set is a collection of objects. - the objects are called the elements of the set. If S is a set, the notation of means that a is an element of S.**Sets & Elements**means that b is not an element of S. Ex1. If Z represents the set of integers, then but**Notation of Sets**• Braces { } - The set A that consists of positive integers less than 7 is • Set-builder notation – • Interval notation – These are sets of real numbers and correspond geometrically to line segments.**Union of Sets**• If S and T are sets, then , represents their union. The union of sets consists of all elements in both sets. Ex 2. Find if**Intersection of Sets**• The intersection of S and T is the set consisting of all elements that are in both sets. It is only what they have in common. Ex 3. Find if**CLASS WORK**If find: 5. 6. 7.**CLASS WORK**If find 8. 9. 10.**Intervals**b b**Ex. 5 Express each interval in terms of inequalities then**graph the interval. • [-1, 2) • [1.5, 4] • (-3, )**CLASS WORK**Express each interval in terms of inequalities then graph the interval. 11. [2, 8) • (-, -5)**CLASS WORK**Express the inequality in interval notation, then graph the interval. 13. 14.