Summary 111 x, y, z, a, b 2, 3, p √2 √7 4 2 1 0 1 2 3 4 5 6 5, 5 2 , 0.5, 0.3 17, 12, p 5 52 6 5 4 3 0.3 0 0.5 – Examples Example 1 Variables: Constants: Expressions: Example 2 0, and 4 are integers. and are rational numbers. and are irrational numbers. Example 3 All real numbers can be located on the real number line. Example 4 “5 is less than 7.” “ is greater than .” “y is less than or equal to 3.4.” “x is greater than or equal to .” 5 6 7 2 7 10 2 10 y 3.4 Example 5 5 and 5 are opposites. Example 6 07 0 7 07 0 7 12 x 12 2x 5, 3a b2 Chapter 1 Summary Key Concepts A variable is a symbol or letter used to represent an unknown number. A constant is a value that is not variable. An algebraic expression is a collection of variables and constants under algebraic operations. Natural numbers: 51, 2, 3, . . .6 Whole numbers: 50, 1, 2, 3, . . .6 Integers: 5. . . 3, 2, 1, 0, 1, 2, 3, . . .6 Rational numbers: The set of numbers that can be expressed in the form where p and q are integers and q does not equal 0. In decimal form, rational numbers are terminating or repeating decimals. Irrational numbers: A subset of the real numbers whose elements cannot be written as a ratio of two integers. In decimal form, irrational numbers are nonterminating, nonrepeating decimals. Real numbers: The set of both the rational numbers and the irrational numbers. “a is less than b.” “a is greater than b.” “a is less than or equal to b.” “a is greater than or equal to b.” a 6 b a 7 b a b Two numbers that are the same distance from zero but on opposite sides of zero on the number line are called opposites. The opposite of a is denoted a. The absolute value of a real number, a, denoted is the distance between a and 0 on the number line. If a 0, 0a 0 a If a 6 0, 0a 0 a 0a 0, a b p q, Introduction to Algebra and the Set of Real Numbers Section 1.1
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