Set-Builder Notation

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# Set-Builder Notation - PowerPoint PPT Presentation

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 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
• 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
• This means “the set of number x such that…”
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 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 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 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 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
• {1, 2, 3, 4, 5, …}
• x ≤ 3
• -4 < x ≤ 14
• All multiple of ∏