# Student Notes - Number Sets, Set and Interval Notation Notes 1819.pdf

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Number Sets , Set & Interval Notes Number Set Symbol Definition Real A real number is a value that can be represented as a quantity on a continuous number line . Rational A rational number is any quantity that can be expressed as the ratio of two integers . Ex: 4 (since 4 = 8 2 ) , 1.2 (since 1.2 = 12 10 = 6 5 ) , - 9 (since 9 = 3 = 3 1 , etc . Irrational An irrational number is any quantity that can NOT be expressed as a fraction (any nonrepeating & nonterminating decimal) Ex: π , e , 2 Integers The set of integers contains whole numbers , negative whole numbers and zero . {… -3, -2, -1, 0, 1, 2, 3 …} Whole Whole numbers are nonnegative integers { 0, 1, 2, 3 …} Natural Natural numbers are positive integers . This set is commonly referred to as the “counting” numbers set . { 1, 2, 3 …} Digits A digit is any number that can be found in a phone number . { 0, 1, 2 9 } ex 1 : List all sets to which each number belongs . a) 2 b) 4 9 c) π 3 ( ) 2 d) 4 Set & Interval Notation Set Notation - A Set is a collection of things (usually numbers) . Example: { 5, 7, 11 } is a set . But we can also "build" a set by describing what is in it . Here is a simple example of set - builder notation: ex  #### You've reached the end of your free preview.

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Unformatted text preview: 2 : Express each set of numbers in set notation . a) n ≤ 40 b) domain: the set of real numbers c) range: the set of integers d) 3 x + 4 ≠ 1 2 e) z &lt; 2 or z ≥ 5 f) z &lt; 2 and z ≥ 5 g) z &gt; 2 and z ≤ 5 Interval Notation -A notation for representing an interval as a pair of numbers . The numbers are the endpoints of the interval . *Parentheses and/or brackets are used to show whether the endpoints are excluded or included . Parentheses , ( ) , indicate a quantity is_________________________ . Brackets , [ ] , indicate a quantity is____________________________ . When using infinity or negative infinity always use_____________________________ . Examples of interval notation: 1,3 ( ) − 1 2 ,0 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ − 4,7 ( ⎤ ⎦ 5,6 ⎡ ⎣ ) 1, ∞ ( ) −∞ ,0 ( ⎤ ⎦ ex 3 : Express each set of numbers in interval notation . a) b) c) d) e) 2 &lt; x ≤ 6 f) x &gt; 30 g) y ≤ 40 h) the set of real numbers i) the set of whole numbers j) no greater than -25 k) z ≤ 6 or z &gt; 17 l) z ≤ 6 and z &gt; 17 m) n = 3 n) n ≠ 3...
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