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Set builder notation is a concise way to describe a set by specifying the properties that its members must satisfy. It is particularly useful for representing sets with a large or infinite number of elements.
Definition and Symbols
Set builder notation uses a variable, a vertical line or colon, and a condition that the elements must satisfy. For example, the set of all natural numbers greater than 5 can be written as:
A = { x | x ∈ ℕ, x > 5 }This reads as "A is the set of all x such that x is a natural number and x is greater than 5"1.
Examples
Here are some examples of sets written in set builder notation:
Set of Even Natural Numbers Less Than 15:
A = { x | x ∈ ℕ, x is even, and x < 15 }This represents the set {2, 4, 6, 8, 10, 12, 14}2.
Set of Rational Numbers:
Q = { p/q | p, q ∈ ℤ, q ≠ 0 }This represents the set of all rational numbers, where p and q are integers and q is not zero2.
Set of Real Numbers Between 2 and 6:
B = { x | x ∈ ℝ, 2 ≤ x ≤ 6 } Set-Builder Notation - Math is Fun
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