Because we will often be dealing with sets such as domain or range of functions, it is convenient to have a collection of symbols to denote certain special subsets called intervals. Interval Interval Notation \(\{x \in \mathbb{R}: a < x < b \}\) \((a,b)\) \(\{x \in \mathbb{R}: a < x \le b \}\) \((a,b]\) \(\{x \in \mathbb{R}: a \le x < b \}\) \([a,b)\) \(\{x \in \mathbb{R}: a \le x \le b \}\) \([a,b]\) \(\{x \in \mathbb{R}: a < x \}\) \((a,\infty)\) \(\{x \in \mathbb{R}: a \le x \}\) \([a,\infty)\) \(\{x \in \mathbb{R}: x < b \}\) \((-\infty,b)\) \(\{x \in \mathbb{R}: x \le b \}\) \((-\infty,b]\) \(\mathbb{R}\) \((-\infty,\infty)\) \(\{x \in \mathbb{R}: a\le x \le b \text{ or}\hspace{0.5em} c < x < d \}\) \( [a,b] \cup (c,d)\) \(\{x \in \mathbb{R}: x < a \text{ or}\hspace{0.5em} b \le x < d \}\) \( (-\infty,a) \cup [b,d) \) The following symbols are often used to abbreviate the corresponding sets: Set Set Symbol Empty set \(\emptyset\) The set of natural numbers or non-negative integers \( \mathbb{N}\) or \(\mathbb{Z}^+_0\) The set of integers \( \mathbb{Z}\) The set of positive integers \( \mathbb{Z}^+\) The set of negative integers \(\mathbb{Z}^-\) The set of rational numbers \(\mathbb{Q}\) The set of real numbers \(\mathbb{R}\) The set of complex numbers \(\mathbb{C}\)

Various intervals of real numbers

IB Year 5 | Grade 11

Because we will often be dealing with sets such as domain or range of functions, it is convenient to have a collection of symbols to denote certain special subsets called intervals.

Interval	Interval Notation
\(\{x \in \mathbb{R}: a < x < b \}\)	\((a,b)\)
\(\{x \in \mathbb{R}: a < x \le b \}\)	\((a,b]\)
\(\{x \in \mathbb{R}: a \le x < b \}\)	\([a,b)\)
\(\{x \in \mathbb{R}: a \le x \le b \}\)	\([a,b]\)
\(\{x \in \mathbb{R}: a < x \}\)	\((a,\infty)\)
\(\{x \in \mathbb{R}: a \le x \}\)	\([a,\infty)\)
\(\{x \in \mathbb{R}: x < b \}\)	\((-\infty,b)\)
\(\{x \in \mathbb{R}: x \le b \}\)	\((-\infty,b]\)
\(\mathbb{R}\)	\((-\infty,\infty)\)
\(\{x \in \mathbb{R}: a\le x \le b \text{ or}\hspace{0.5em} c < x < d \}\)	\( [a,b] \cup (c,d)\)
\(\{x \in \mathbb{R}: x < a \text{ or}\hspace{0.5em} b \le x < d \}\)	\( (-\infty,a) \cup [b,d) \)

The following symbols are often used to abbreviate the corresponding sets:

Set	Set Symbol
Empty set	\(\emptyset\)
The set of natural numbers or non-negative integers	\( \mathbb{N}\) or \(\mathbb{Z}^+_0\)
The set of integers	\( \mathbb{Z}\)
The set of positive integers	\( \mathbb{Z}^+\)
The set of negative integers	\(\mathbb{Z}^-\)
The set of rational numbers	\(\mathbb{Q}\)
The set of real numbers	\(\mathbb{R}\)
The set of complex numbers	\(\mathbb{C}\)

Create a free account to practise similar questions.

Create free account Sign in IB Math tuition

Need help? Join our JC Math tuition classes.

Learn more