<p>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 <strong>intervals</strong>.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: left; --cell-justify: flex-start"><p><strong>Interval</strong></p></th><th style="text-align: left; --cell-justify: flex-start"><p><strong>Interval Notation</strong></p></th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start"><p>\(\{x \in \mathbb{R}: a &lt; x &lt; b \}\)</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\((a,b)\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>\(\{x \in \mathbb{R}: a &lt; x \le b \}\)</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\((a,b]\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>\(\{x \in \mathbb{R}: a \le x &lt; b \}\)</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\([a,b)\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>\(\{x \in \mathbb{R}: a \le x \le b \}\)</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\([a,b]\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>\(\{x \in \mathbb{R}: a &lt; x \}\)</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\((a,\infty)\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>\(\{x \in \mathbb{R}: a \le x \}\)</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\([a,\infty)\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>\(\{x \in \mathbb{R}: x &lt; b \}\)</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\((-\infty,b)\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>\(\{x \in \mathbb{R}: x \le b \}\)</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\((-\infty,b]\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>\(\mathbb{R}\)</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\((-\infty,\infty)\)</p></td></tr></tbody></table></div></div>
<p>It is also convenient to use the set union symbol to help us express the disjoint union of two intervals; for example, <br>\[
(0,1] \cup [2,3).
\]</p>
<p>The following symbols are often used to abbreviate the corresponding sets:<br></p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: left; --cell-justify: flex-start"><p><strong>Set</strong></p></th><th style="text-align: left; --cell-justify: flex-start"><p><strong>Set Symbol</strong></p></th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start"><p>Empty set</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\(\emptyset\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>The set of natural numbers or non-negative integers</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\( \mathbb{N}\) or \(\mathbb{Z}^+_0\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>The set of integers</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\( \mathbb{Z}\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>The set of positive integers</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\( \mathbb{Z}^+\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>The set of negative integers</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\(\mathbb{Z}^-\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>The set of rational numbers</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\(\mathbb{Q}\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>The set of real numbers</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\(\mathbb{R}\)</p></td></tr><tr><td style="text-align: left; --cell-justify: flex-start"><p>The set of complex numbers</p></td><td style="text-align: left; --cell-justify: flex-start"><p>\(\mathbb{C}\)</p></td></tr></tbody></table></div></div>

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**.

It is also convenient to use the set union symbol to help us express the disjoint union of two intervals; for example, 
\[
(0,1] \cup [2,3).
\]

Various intervals of real numbers

Various intervals of real numbers