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Set-Builder Notation. Set-Builder Notation. {x|-3 ≤ x ≤ 16, x ∈ ℤ}. The set of numbers such that…. x is greater than or equal to -3 and less than or equal to 16. And x is an element of the set of integers. Set-Builder Notation.

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set builder notation1
Set-Builder Notation
  • {x|-3 ≤ x ≤ 16, x ∈ ℤ}

The set of numbers such that…

x is greater than or equal to -3 and less than or equal to 16

And x is an element of the set of integers

set builder notation2
Set-Builder Notation
  • Describe the set of numbers using set-builder 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…”
set builder notation3
Set-Builder Notation
  • Describe the set of numbers using set-builder 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
set builder notation4
Set-Builder Notation
  • Describe the set of numbers using set-builder 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
set builder notation5
Set-Builder Notation
  • Describe the set of numbers using set-builder 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
set builder notation6
Set-Builder Notation
  • 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}
set builder notation7
Set-Builder Notation
  • 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}
practice
Practice
  • {1, 2, 3, 4, 5, …}
  • x ≤ 3
  • -4 < x ≤ 14
  • All multiple of ∏
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