Mth141S12n - Sec. 1.2 Introduction to Relations and...

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Unformatted text preview: Sec. 1.2 Introduction to Relations and Functions This section starts out with some notation discussion about how we can refer to a group of numbers on the number line. Say , for example, we wanted to indicate the numbers greater than 2. We could do this in various ways: a) use an algebraic inequality 2 x x is greater than 2 b) use set notation { | 2} x x the set of all x such that x is greater then 2 c) use graph on the number line all numbers to the right of 2, not including 2 d) use interval notation ( 29 2, + all numbers from 2 to positive infinity, not including 2 Ex. Show all numbers between -3 and 7 : a) use an algebraic inequality b) use set notation c) use graph on the number line d) use interval notation Example1: a) x is greater than 3 x > 3 b) the set of all x such that x is greater than 3 {x | x > 3} c) all the numbers greater than 3 on the number line d) all the numbers from 3 to positive infinity, not including 3. ( 3, ) + Example 2: a) x is less than or equal to 2 2 x b) the set of all x such that x is less than or equal to 2 { } | 2 x x c) all the numbers less than or equal to 2 on the number line d) all the numbers from negative infinity to 2 , including 2. ] ( ,2- Example 3: All real numbers can be shown as: a) x is a member of the real numbers x R b) the set of all numbers x such that x is a member of the real numbers { | x x R } c) all numbers on the real number line d) all real numbers ( 29 ,- + Note : An interval is said to be an open interval if it does not include the endpoints, and a closed interval if it does include the endpoints. A half-open interval (or half-closed interval) includes the endpoint on one end, but not on the other. An unbounded interval extends to an infinity on one end, or both ends....
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Mth141S12n - Sec. 1.2 Introduction to Relations and...

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