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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) algebraic inequality 2 x “x is greater than 2” b) set notation {  2} x x “the set of all x such that x is greater then 2” c) number line graph “all numbers to the right of 2, not including 2” d) 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 } where R is the set of all real numbers 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 “halfopen interval” (or “halfclosed 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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 Fall '06
 Lebre
 Algebra, Set Theory, Topology, line graph, Order theory, Complex number

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