set-builder notation
{x| a < x < b} or {x| x ≥ 0}*Domain = x & Range = y
Set-builder notation, also known as set comprehension notation or set description notation, is a way to represent or define a set of elements by providing a rule or condition that describes the members or elements of the set. In set-builder notation, the set is represented within curly brackets, and the rule or condition is given after a vertical bar.
The general form of set-builder notation is:
{variable | rule/condition}
Here, variable refers to the variable(s) used in the rule or condition, and rule/condition specifies the requirements for the elements that belong to the set.
For example, suppose we want to define the set of even integers. We could use set-builder notation as follows:
{ x | x is an even integer }
This reads as the set of all x such that x is an even integer, and the notation represents the set { 2, 4, -6, 8, … }.
Another example is defining the set of all natural numbers that are less than 10. We could use set-builder notation as:
{ x | x is a natural number and x < 10 } This reads as the set of all x such that x is a natural number and x is less than 10, and the notation represents the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 }.
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