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{x|-3 ≤ x ≤ 16, x ∈ ℤ} Describe the set of numbers using setbuilder notation. {8, 9, 10, 11, 12, …} The set of numbers is always considered x unless otherwise stated So we start with: {x| ◦ This means “the set of number x such that…” Describe the set of numbers using setbuilder notation. {8, 9, 10, 11, 12, …} This set only has numbers starting at 8 and increasing We write that as an inequality: x ≥ 8 This includes all the numbers in the set! At this point we have: {x| x ≥ 8 Describe the set of numbers using setbuilder notation. {8, 9, 10, 11, 12, …} We now have to state what set of number x is an element of Since these numbers are positive whole numbers, the set is W ◦ We can write this as x ∈ W Describe the set of numbers using setbuilder notation. {8, 9, 10, 11, 12, …} We can then put everything together for the final answer: {x| x ≥ 8, x ∈ W} Verbally this reads: The set of all x such that x is greater than or equal to 8 and x is an element of the set of whole numbers Example 2: Write the following in set-builder notation: x < 7 There’s no stipulation on the numbers as long as they’re less than 7, so it can be all real numbers Therefore: {x| x < 7, x ∈ ℝ} Example 3: All multiples of 3 In this case, x is equal to 3 times any number ◦ We write this as x = 3n In this case, multiples of 3 can only be an integer (positive or negative whole numbers or zero) {x| x = 3n, x ∈ ℤ} 1. {1, 2, 3, 4, 5, …} 2. x≤3 3. -4 < x ≤ 14 4. All multiple of ∏