Notes
| \({\text{Sets of Numbers}}\) | ||
| \(\underline{\text{Letter}}\) | \(\underline{\text{Set}}\) | \(\underline{\text{Examples}}\) |
|---|---|---|
Set Builder Notation Examples
\(\{x| x \lt8,x \in {\displaystyle \mathbb {R} }\}\)
\(\{x|-5\le x \le15,x \in {\displaystyle \mathbb {Z} }\}\)
\(\{x| x \ge4,x \in {\displaystyle \mathbb {N} }\}\)
Practice Questions
Convert each from interval notation to set-builder notation
\( (-\infty,3) \)
\([-8,5) \)
\([-4,\infty)\)
\([-8,10]\)
\((-\infty,2]\)
\((5,20]\)
\((15,\infty)\)
See Related Pages\(\)
\(\bullet\text{ Interval Notation}\)
\(\,\,\,\,\,\,\,\,(-\infty,4)\) U \((8,\infty)\)
In Summary
Set builder notation is a mathematical notation used to define a set in terms of properties that its elements must satisfy. This type of notation is typically used when the elements of a set cannot be listed explicitly, or when it is more convenient to describe the set in terms of its properties.
In set builder notation, a set is defined by specifying a variable, such as x, that represents the elements of the set, and then providing a condition that the elements must satisfy.
Set builder notation is useful because it provides a compact and intuitive way to define sets that cannot be listed explicitly. It is also useful for expressing relationships between sets and for proving mathematical statements involving sets. To use set builder notation effectively, it is important to carefully specify the variable and the condition that the elements must satisfy.