Ch01pgs001 014
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Ch01pgs001 014
IJa.1 I ỉornsby X 1c( i ĩ I ì IÌ isFORCOLLEGE STUDENTSI •' i I t H I *'. < 111 i < > 112 CHAPIÍR I Review of the Real Number SystemmBasic ConceptsOBJE Ch01pgs001 014 ECTIVES1Write sets using set notation.2Use number lines.3Know the common sets of numbers.4Find additive inverses.5Use absolute value.6Use Inequality symbols.7Graph sets of real numbers.In this chapter we review some of the basic symbols and rules of algebra.OBJECTIVE 1 Write sets using set notation. Ch01pgs001 014 A Ise ths a collection of objects called the [elements 01 members|of the set. In algebra, the elements of a set are usually numbers. Set braces. I Ỉ.Ch01pgs001 014
are used to enclose the elements. For example. 2 is an element of the set {1, 2.3}. Since we can count the number of elements in the set {1. 2. 3}. IIJa.1 I ỉornsby X 1c( i ĩ I ì IÌ isFORCOLLEGE STUDENTSI •' i I t H I *'. < 111 i < > 112 CHAPIÍR I Review of the Real Number SystemmBasic ConceptsOBJE Ch01pgs001 014 the counting numbers.[The three dots show that the list continues in the same pattern indetmitely. We cannot list all of the elements of the set of natural numbers, so It is an infinite set._______When 0 is included with the set of natural numbers, we have the set of [whole I Ịnumbersl writtenIF - { Ch01pgs001 014 o, 1.2. 3.4. 5, 6....}.A set containing no elements, such as the set of whole numbers less than 0. IS called the [empty set, or null set.Ịusually writCh01pgs001 014
ten 0 or 1 }.CAUTION Do not write {0} for the empty' set; {0} is a set with one element.0. Use the notation 0 or í 5 for the empty set.To write the faIJa.1 I ỉornsby X 1c( i ĩ I ì IÌ isFORCOLLEGE STUDENTSI •' i I t H I *'. < 111 i < > 112 CHAPIÍR I Review of the Real Number SystemmBasic ConceptsOBJE Ch01pgs001 014 tural numbers .V. so we may write2 e .V.To show that 0 is not an element of set jV. we draw a slash through the symbol E.0€ NTwo sets are equal if they contain exactly the same elements. For example. {1. 2} — {2. 1}. because the sets contain the same elements. (Order doesn’t matter.) On the other ha Ch01pgs001 014 nd. {1. 2}{o. 1. 2} means "is not equal to”) since one set con-tains the element 0 while the other does not.In algebra, letters called|variables|are oCh01pgs001 014
ften used to represent numbers or to define sets of numbers. For example.{v|.v is a natural number between 3 and 15}(read “the set of all elements V sIJa.1 I ỉornsby X 1c( i ĩ I ì IÌ isFORCOLLEGE STUDENTSI •' i I t H I *'. < 111 i < > 112 CHAPIÍR I Review of the Real Number SystemmBasic ConceptsOBJEIJa.1 I ỉornsby X 1c( i ĩ I ì IÌ isFORCOLLEGE STUDENTSI •' i I t H I *'. < 111 i < > 112 CHAPIÍR I Review of the Real Number SystemmBasic ConceptsOBJEGọi ngay
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