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Section 1.1 – Sets of Numbers: Objectives (California Algebra 1 Standard: 1) • Classify and order real numbers Vocabulary:

Set:

A set is a collection of items called elements.

Subset: A subset is a set whose elements all belong to one or more other sets. Empty Set: The empty set denoted with the symbol ∅ is a set containing no elements. Roster Notation:

Using roster notation, the elements of a set are listed between braces.

Example: {1, 2, 3, 4, 5, 6} Finite Set:

A finite set has a definite – or finite – number of elements. The set above is an example of a finite set.

Infinite Set: An infinite set has an unlimited – or undefined - number of elements. Example: {1, 2, 3, 4, 5 ….} Interval Notation:

An interval is the set of all numbers between two endpoints, such as 3 and 5. In interval notation the symbols [ and ] are used to include an endpoint in an interval, and the symbols ( and ) are used to exclude an endpoint from an interval.

Example: (3, 5) represents the set of all numbers between – but not including – 3 and 5. [9, 100] represents the set of all numbers between – and including – 9 and 100.


Set-Builder Notation: Set-Builder Notation uses the properties of the elements in the set to define the set. Inequalities and the element symbol (â&#x2C6;&#x2C6;) are often used in set-builder notation. The set {9, 10, 11, 12, 13, 14, 15} is represented below in set-builder notation. The set of all numbers x such that x has the given properties đ?&#x2019;&#x2122;    đ?&#x;&#x2013; < đ?&#x2019;&#x2122; â&#x2030;¤ đ?&#x;?đ?&#x;&#x201C;    đ?&#x2019;&#x201A;đ?&#x2019;?đ?&#x2019;&#x2026;    đ?&#x2019;&#x2122; â&#x2C6;&#x2C6; â&#x201E;&#x2022;} !

Example 1: Consider the numbers 0. 6, 2, 0, â&#x2C6;&#x2019; ! , 0.5129 a.) Order the numbers from least to greatest

b.) Classify each number by the subsets of real numbers to which it belongs.

Example 2: Consider the numbers â&#x2C6;&#x2019;2, đ?&#x153;&#x2039;, â&#x2C6;&#x2019;0.321,

!

a.) Order the numbers from least to greatest which it belongs.

b.) Classify each number by the subsets of real numbers to

!

 đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x2018; â&#x2C6;&#x2019; 3

Example 3 â&#x20AC;&#x201C; Use Interval notation to represent each set of numbers: a.) 4   â&#x2030;¤ đ?&#x2018;Ľ   < 6

b.)

c.) đ?&#x2018;Ľ   â&#x2030;¤ 2  đ?&#x2018;&#x153;đ?&#x2018;&#x;  3 < đ?&#x2018;Ľ   â&#x2030;¤ 11

d.)

Example 4 â&#x20AC;&#x201C; Rewrite each set in the indicated notation: a.) đ?&#x2019;&#x2122;    đ?&#x2019;&#x2122; = đ?&#x;?đ?&#x2019;?    đ?&#x2019;&#x201A;đ?&#x2019;?đ?&#x2019;&#x2026;    đ?&#x2019;? â&#x2C6;&#x2C6; â&#x201E;&#x2022;} ; words

c.)

e.) đ?&#x2019;&#x2122;    đ?&#x;? < đ?&#x2019;&#x2122; < đ?&#x;&#x2013;    đ?&#x2019;&#x201A;đ?&#x2019;?đ?&#x2019;&#x2026;    đ?&#x2019;&#x2122; â&#x2C6;&#x2C6; â&#x201E;&#x2022;}

b.) Numbers and symbols on a telephone keyboard ; roster notation

; set-builder notation

d.) {2, 4, 6, 8} ; words

f.) [99, â&#x2C6;&#x17E;); set-builder notation

Homework: Pages 10 â&#x20AC;&#x201C; 12 # 13 â&#x20AC;&#x201C; 61 odds only


Algebra 1 Section 1.1 Notes