<!DOCTYPE html>
<html class="client-nojs vector-feature-night-mode-disabled vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-sticky-header-enabled" lang="en" dir="ltr"><head>
<meta charset="UTF-8">
<title>Constant function</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="canonical" href="https://en.wikipedia.org/wiki/Constant_function"> <link href="./mw/ext.cite.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/ext.math.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/skins.vector.icons.css" rel="stylesheet" type="text/css">
<link href="./mw/skins.vector.search.codex.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/skins.vector.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/user.styles.css" rel="stylesheet" type="text/css">
<meta name="ResourceLoaderDynamicStyles" content="">
<link rel="stylesheet" type="text/css" href="./mw/site.styles.css">
<link rel="stylesheet" type="text/css" href="./mw/noscript.css">
<link rel="stylesheet" type="text/css" href="./footer.css">
<link rel="stylesheet" type="text/css" href="./vector-2022.css">
</head>
<body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Constant_function rootpage-Constant_function skin-vector-2022 action-view">
<div class="mw-page-container">
<div class="mw-page-container-inner">
<div class="mw-content-container">
<main id="content" class="mw-body">
<header class="mw-body-header vector-page-titlebar">
<h1 id="firstHeading" class="firstHeading mw-first-heading">
<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Constant function</span></span>
</h1>
</header>
<a id="top"></a>
<div id="bodyContent" class="vector-body ve-init-mw-desktopArticleTarget-targetContainer" aria-labelledby="firstHeading" data-mw-ve-target-container="">
<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr">
<style data-mw-deduplicate="TemplateStyles:r1236090951">
/* start https://en.wikipedia.org/ */
.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}
/* end https://en.wikipedia.org/ */
</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="Function_constant" class="mw-redirect" title="Function constant">function constant</a>.</div>
<style data-mw-deduplicate="TemplateStyles:r1129693374">
/* start https://en.wikipedia.org/ */
.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" Β· ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}
/* end https://en.wikipedia.org/ */
</style><style data-mw-deduplicate="TemplateStyles:r1246091330">
/* start https://en.wikipedia.org/ */
.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}
/* end https://en.wikipedia.org/ */
</style><table class="sidebar nomobile nowraplinks"><tbody><tr><th class="sidebar-title" style="letter-spacing:0.0125em; background-color:#FFCC99"><a href="Function_(mathematics)" title="Function (mathematics)">Function</a></th></tr><tr><td class="sidebar-image"><span class="texhtml texhtml-big" style="font-size:250%;"><i>x</i> β¦ <i>f</i>β(<i>x</i>)</span></td></tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px">
<a href="History_of_the_function_concept" title="History of the function concept">History of the function concept</a></th></tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px">
Types by <a href="Domain_of_a_function" title="Domain of a function">domain</a> and <a href="Codomain" title="Codomain">codomain</a></th></tr><tr><td class="sidebar-content">
<div class="hlist">
<ul><li><a href="Boolean-valued_function" title="Boolean-valued function"><span class="texhtml"><span title="arbitrary set"><var>X</var></span> β <span title="Codomain of Booleans">πΉ</span></span></a></li>
<li><a href="Ordered_pair" title="Ordered pair">
<span class="texhtml"><span title="Domain of Booleans">πΉ</span>
β <span title="arbitrary set"><var>X</var></span></span></a></li>
<li><a href="Boolean_function" title="Boolean function">
<span class="texhtml"><span title="several Boolean variables">πΉ<sup><var>n</var></sup></span>
β <span title="Codomain of natural numbers"><var>X</var></span></span></a></li>
<li><a href="Integer-valued_function" title="Integer-valued function">
<span class="texhtml"><span title="arbitrary set"><var>X</var></span>
β <span title="integers">β€</span></span></a></li>
<li><a href="Sequence" title="Sequence">
<span class="texhtml"><span title="integers">β€</span>
β <span title="arbitrary set"><var>X</var></span></span></a></li>
<li><a href="Real-valued_function" title="Real-valued function">
<span class="texhtml"><span title="arbitrary set"><var>X</var></span>
β <span title="real numbers">β</span></span></a></li>
<li><a href="Function_of_a_real_variable" title="Function of a real variable">
<span class="texhtml"><span title="real numbers">β</span>
β <span title="arbitrary set"><var>X</var></span></span></a></li>
<li><a href="Function_of_several_real_variables" title="Function of several real variables">
<span class="texhtml"><span title="real coordinate (or Euclidean) space">β<sup><var>n</var></sup></span>
β <span title="arbitrary set"><var>X</var></span></span></a></li>
<li><a href="Complex-valued_function" class="mw-redirect" title="Complex-valued function">
<span class="texhtml"><span title="arbitrary set"><var>X</var></span>
β <span title="complex numbers">β</span></span></a></li>
<li><a href="Function_of_a_complex_variable" class="mw-redirect" title="Function of a complex variable">
<span class="texhtml"><span title="complex numbers">β</span>
β <span title="arbitrary set"><var>X</var></span></span></a></li>
<li><a href="Function_of_several_complex_variables" title="Function of several complex variables">
<span class="texhtml"><span title="complex coordinate space">β<sup><var>n</var></sup></span>
β <span title="arbitrary set"><var>X</var></span></span></a></li></ul>
</div></td>
</tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px">
β<a href="List_of_types_of_functions" title="List of types of functions">Classes/properties</a>β</th></tr><tr><td class="sidebar-content">
<div class="hlist">
<ul>
<li><a href="Identity_function" title="Identity function">Identity</a></li>
<li><a href="Linear_map" title="Linear map">Linear</a></li>
<li><a href="Polynomial" title="Polynomial">Polynomial</a></li>
<li><a href="Rational_function" title="Rational function">Rational</a></li>
<li><a href="Algebraic_function" title="Algebraic function">Algebraic</a></li>
<li><a href="Analytic_function" title="Analytic function">Analytic</a></li>
<li><a href="Smooth_function" class="mw-redirect" title="Smooth function">Smooth</a></li>
<li><a href="Continuous_function" title="Continuous function">Continuous</a></li>
<li><a href="Measurable_function" title="Measurable function">Measurable</a></li>
<li><a href="Injective_function" title="Injective function">Injective</a></li>
<li><a href="Surjective_function" title="Surjective function">Surjective</a></li>
<li><a href="Bijection" title="Bijection">Bijective</a></li></ul>
</div></td>
</tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px">
ββConstructions</th></tr><tr><td class="sidebar-content">
<div class="hlist">
<ul><li><a href="Restriction_(mathematics)" title="Restriction (mathematics)">Restriction</a></li>
<li><a href="Function_composition" title="Function composition">Composition</a></li>
<li><a href="Lambda_calculus" title="Lambda calculus">Ξ»</a></li>
<li><a href="Inverse_function" title="Inverse function">Inverse</a></li></ul>
</div></td>
</tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px">
ββGeneralizationsββ</th></tr><tr><td class="sidebar-content">
<div class="hlist">
<ul><li><a href="Relation_(mathematics)" title="Relation (mathematics)">Relation</a> (<a href="Binary_relation" title="Binary relation">Binary relation</a>)</li>
<li><a href="Set-valued_function" title="Set-valued function">Set-valued</a></li>
<li><a href="Multivalued_function" title="Multivalued function">Multivalued</a></li>
<li><a href="Partial_function" title="Partial function">Partial</a></li>
<li><a href="Implicit_function" title="Implicit function">Implicit</a></li>
<li><a href="Function_space" title="Function space">Space</a></li>
<li><a href="Higher-order_function" title="Higher-order function">Higher-order</a></li>
<li><a href="Morphism" title="Morphism">Morphism</a></li>
<li><a href="Functor" title="Functor">Functor</a></li></ul>
</div></td>
</tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px">
ββ<a href="List_of_mathematical_functions" title="List of mathematical functions">List of specific functions</a></th></tr><tr><td class="sidebar-navbar"><style data-mw-deduplicate="TemplateStyles:r1239400231">
/* start https://en.wikipedia.org/ */
.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}
/* end https://en.wikipedia.org/ */
</style></td></tr></tbody></table>
<p>In <a href="Mathematics" title="Mathematics">mathematics</a>, a <b>constant function</b> is a <a href="Function_(mathematics)" title="Function (mathematics)">function</a> whose (output) value is the same for every input value.
</p>
<meta property="mw:PageProp/toc">
<div class="mw-heading mw-heading2"><h2 id="Basic_properties">Basic properties</h2></div>
<p>As a real-valued function of a real-valued argument, a constant function has the general form <span class="texhtml"><i>y</i>(<i>x</i>) = <i>c</i></span> or just <span class="nowrap"><span class="texhtml"><i>y</i> = <i>c</i></span>.</span> For example, the function <span class="texhtml"><i>y</i>(<i>x</i>) = 4</span> is the specific constant function where the output value is <span class="texhtml"><i>c</i> = 4</span>. The <a href="Domain_of_a_function" title="Domain of a function">domain of this function</a> is the set of all <a href="Real_number" title="Real number">real numbers</a>. The <a href="Image_(mathematics)" title="Image (mathematics)">image</a> of this function is the <a href="Singleton_(mathematics)" title="Singleton (mathematics)">singleton</a> set <span class="texhtml">{4}</span>. The independent variable <span class="nowrap"><i>x</i></span> does not appear on the right side of the function expression and so its value is "vacuously substituted"; namely <span class="texhtml"><i>y</i>(0) = 4</span>, <span class="texhtml"><i>y</i>(β2.7) = 4</span>, <span class="texhtml"><i>y</i>(Ο) = 4</span>, and so on. No matter what value of <span class="texhtml"><i>x</i></span> is input, the output is <span class="texhtml">4</span>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p><p>The graph of the constant function <span class="texhtml"><i>y</i> = <i>c</i></span> is a <i>horizontal line</i> in the <a href="Plane_(geometry)" class="mw-redirect" title="Plane (geometry)">plane</a> that passes through the point <span class="texhtml">(0, <i>c</i>)</span>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In the context of a <a href="Polynomial" title="Polynomial">polynomial</a> in one variable <span class="texhtml"><i>x</i></span>, the constant function is called <i>non-zero constant function</i> because it is a polynomial of degree 0, and its general form is <span class="texhtml"><i>f</i>(<i>x</i>) = <i>c</i></span>, where <span class="texhtml mvar" style="font-style:italic;">c</span> is nonzero. This function has no intersection point with the <span class="nowrap"><span class="texhtml"><i>x</i></span>-</span>axis, meaning it has no <a href="Zero_of_a_function" title="Zero of a function">root (zero)</a>. On the other hand, the polynomial <span class="texhtml"><i>f</i>(<i>x</i>) = 0</span> is the <i>identically zero function</i>. It is the (trivial) constant function and every <span class="texhtml"><i>x</i></span> is a root. Its graph is the <span class="nowrap"><span class="texhtml"><i>x</i></span>-</span>axis in the plane.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Its graph is symmetric with respect to the <span class="nowrap"><span class="texhtml"><i>y</i></span>-</span>axis, and therefore a constant function is an <a href="Even_and_odd_functions" title="Even and odd functions">even function</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>
</p><p>In the context where it is defined, the <a href="Derivative" title="Derivative">derivative</a> of a function is a measure of the rate of change of function values with respect to change in input values. Because a constant function does not change, its derivative is 0.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> This is often written: <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x\mapsto c)'=0}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">β¦<!-- β¦ --></mo>
<mi>c</mi>
<msup>
<mo stretchy="false">)</mo>
<mo>β²</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle (x\mapsto c)'=0}</annotation>
</semantics>
</math></span><img src="./2b70ef5cb5d36d9f6f42c1d342b92a44b2e05f86.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.706ex; height:3.009ex;" alt="{\displaystyle (x\mapsto c)'=0}" loading="lazy"></span>. The converse is also true. Namely, if <span class="texhtml"><i>y</i>β²(<i>x</i>) = 0</span> for all real numbers <span class="texhtml"><i>x</i></span>, then <span class="texhtml"><i>y</i></span> is a constant function.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> For example, given the constant function <span class="nowrap"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(x)=-{\sqrt {2}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>y</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>β<!-- β --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle y(x)=-{\sqrt {2}}}</annotation>
</semantics>
</math></span><img src="./285edec275a468d00d76f0d7802eb9481adc6e45.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.299ex; height:3.176ex;" alt="{\displaystyle y(x)=-{\sqrt {2}}}" loading="lazy"></span>.</span> The derivative of <span class="texhtml"><i>y</i></span> is the identically zero function <span class="nowrap"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y'(x)=\left(x\mapsto -{\sqrt {2}}\right)'=0}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>y</mi>
<mo>β²</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo stretchy="false">β¦<!-- β¦ --></mo>
<mo>β<!-- β --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>β²</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle y'(x)=\left(x\mapsto -{\sqrt {2}}\right)'=0}</annotation>
</semantics>
</math></span><img src="./03b4d2c9fffb1ed038719c927b562e90cbacb6ea.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:25.008ex; height:3.509ex;" alt="{\displaystyle y'(x)=\left(x\mapsto -{\sqrt {2}}\right)'=0}" loading="lazy"></span>.</span>
</p>
<div class="mw-heading mw-heading2"><h2 id="Other_properties">Other properties</h2></div>
<p>For functions between <a href="Preorder" title="Preorder">preordered sets</a>, constant functions are both <a href="Order-preserving" class="mw-redirect" title="Order-preserving">order-preserving</a> and <a href="Order-reversing" class="mw-redirect" title="Order-reversing">order-reversing</a>; conversely, if <span class="texhtml"><i>f</i></span> is both order-preserving and order-reversing, and if the <a href="Domain_of_a_function" title="Domain of a function">domain</a> of <span class="texhtml"><i>f</i></span> is a <a href="Lattice_(order)" title="Lattice (order)">lattice</a>, then <span class="texhtml"><i>f</i></span> must be constant.
</p>
<ul><li>Every constant function whose <a href="Domain_of_a_function" title="Domain of a function">domain</a> and <a href="Codomain" title="Codomain">codomain</a> are the same set <span class="texhtml"><i>X</i></span> is a <a href="Left_zero" class="mw-redirect" title="Left zero">left zero</a> of the <a href="Full_transformation_monoid" class="mw-redirect" title="Full transformation monoid">full transformation monoid</a> on <span class="texhtml"><i>X</i></span>, which implies that it is also <a href="Idempotent" class="mw-redirect" title="Idempotent">idempotent</a>.</li>
<li>It has zero <a href="Slope" title="Slope">slope</a> or <a href="Gradient" title="Gradient">gradient</a>.</li>
<li>Every constant function between <a href="Topological_space" title="Topological space">topological spaces</a> is <a href="Continuous_function_(topology)" class="mw-redirect" title="Continuous function (topology)">continuous</a>.</li>
<li>A constant function factors through the <a href="Singleton_(mathematics)" title="Singleton (mathematics)">one-point set</a>, the <a href="Terminal_object" class="mw-redirect" title="Terminal object">terminal object</a> in the <a href="Category_of_sets" title="Category of sets">category of sets</a>. This observation is instrumental for <a href="F._William_Lawvere" class="mw-redirect" title="F. William Lawvere">F. William Lawvere</a>'s axiomatization of set theory, the <a href="Elementary_Theory_of_the_Category_of_Sets" title="Elementary Theory of the Category of Sets">Elementary Theory of the Category of Sets</a> (ETCS).<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li>
<li>For any non-empty <span class="texhtml"><i>X</i></span>, every set <span class="texhtml"><i>Y</i></span> is <a href="Isomorphic" class="mw-redirect" title="Isomorphic">isomorphic</a> to the set of constant functions in <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X\to Y}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>X</mi>
<mo stretchy="false">β<!-- β --></mo>
<mi>Y</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle X\to Y}</annotation>
</semantics>
</math></span><img src="./290b16963d52e4a7995aae01ee854b97a6ea10c0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.367ex; height:2.176ex;" alt="{\displaystyle X\to Y}" loading="lazy"></span>. For any <span class="texhtml"><i>X</i></span> and each element <span class="texhtml"><i>y</i></span> in <span class="texhtml"><i>Y</i></span>, there is a unique function <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {y}}:X\to Y}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>y</mi>
<mo stretchy="false">~<!-- ~ --></mo>
</mover>
</mrow>
</mrow>
<mo>:</mo>
<mi>X</mi>
<mo stretchy="false">β<!-- β --></mo>
<mi>Y</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\tilde {y}}:X\to Y}</annotation>
</semantics>
</math></span><img src="./b5c1a8cc5d094e9b2a4f517f18bdb00d8a3d774e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.607ex; height:2.509ex;" alt="{\displaystyle {\tilde {y}}:X\to Y}" loading="lazy"></span> such that <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {y}}(x)=y}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>y</mi>
<mo stretchy="false">~<!-- ~ --></mo>
</mover>
</mrow>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>y</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\tilde {y}}(x)=y}</annotation>
</semantics>
</math></span><img src="./def160f3fbd9539fcd6cf3667456a68b7a670e81.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.695ex; height:2.843ex;" alt="{\displaystyle {\tilde {y}}(x)=y}" loading="lazy"></span> for all <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\in X}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>x</mi>
<mo>β<!-- β --></mo>
<mi>X</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x\in X}</annotation>
</semantics>
</math></span><img src="./3e580967f68f36743e894aa7944f032dda6ea01d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.15ex; height:2.176ex;" alt="{\displaystyle x\in X}" loading="lazy"></span>. Conversely, if a function <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:X\to Y}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>f</mi>
<mo>:</mo>
<mi>X</mi>
<mo stretchy="false">β<!-- β --></mo>
<mi>Y</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f:X\to Y}</annotation>
</semantics>
</math></span><img src="./abd1e080abef4bbdab67b43819c6431e7561361c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.583ex; height:2.509ex;" alt="{\displaystyle f:X\to Y}" loading="lazy"></span> satisfies <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=f(x')}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<msup>
<mi>x</mi>
<mo>β²</mo>
</msup>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f(x)=f(x')}</annotation>
</semantics>
</math></span><img src="./cfbc55981c8e3a0f06edcb2b2c857a4e682a9dd8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.618ex; height:3.009ex;" alt="{\displaystyle f(x)=f(x')}" loading="lazy"></span> for all <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x,x'\in X}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>x</mi>
<mo>,</mo>
<msup>
<mi>x</mi>
<mo>β²</mo>
</msup>
<mo>β<!-- β --></mo>
<mi>X</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x,x'\in X}</annotation>
</semantics>
</math></span><img src="./1785fb75b6170e9a3e43dde32bd67398b5cd5f19.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.199ex; height:2.843ex;" alt="{\displaystyle x,x'\in X}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>f</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f}</annotation>
</semantics>
</math></span><img src="./132e57acb643253e7810ee9702d9581f159a1c61.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" loading="lazy"></span> is by definition a constant function.
<ul><li>As a corollary, the one-point set is a <a href="Generator_(category_theory)" title="Generator (category theory)">generator</a> in the category of sets.</li>
<li>Every set <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>X</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle X}</annotation>
</semantics>
</math></span><img src="./68baa052181f707c662844a465bfeeb135e82bab.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}" loading="lazy"></span> is canonically isomorphic to the function set <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X^{1}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>X</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle X^{1}}</annotation>
</semantics>
</math></span><img src="./6fca53d8f3bcc5469eece7dc6b23ada615470229.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.051ex; height:2.676ex;" alt="{\displaystyle X^{1}}" loading="lazy"></span>, or <a href="Hom_set" class="mw-redirect" title="Hom set">hom set</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {hom} (1,X)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>hom</mi>
<mo>β‘<!-- β‘ --></mo>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>,</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \operatorname {hom} (1,X)}</annotation>
</semantics>
</math></span><img src="./683f9d3f0d237bd89a774ee61ff251d88a15b862.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.377ex; height:2.843ex;" alt="{\displaystyle \operatorname {hom} (1,X)}" loading="lazy"></span> in the category of sets, where 1 is the one-point set. Because of this, and the adjunction between Cartesian products and hom in the category of sets (so there is a canonical isomorphism between functions of two variables and functions of one variable valued in functions of another (single) variable, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {hom} (X\times Y,Z)\cong \operatorname {hom} (X(\operatorname {hom} (Y,Z))}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>hom</mi>
<mo>β‘<!-- β‘ --></mo>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>Γ<!-- Γ --></mo>
<mi>Y</mi>
<mo>,</mo>
<mi>Z</mi>
<mo stretchy="false">)</mo>
<mo>β
<!-- β
--></mo>
<mi>hom</mi>
<mo>β‘<!-- β‘ --></mo>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">(</mo>
<mi>hom</mi>
<mo>β‘<!-- β‘ --></mo>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo>,</mo>
<mi>Z</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \operatorname {hom} (X\times Y,Z)\cong \operatorname {hom} (X(\operatorname {hom} (Y,Z))}</annotation>
</semantics>
</math></span><img src="./7f84f85092588ccd9859932673778c3bc3e02b34.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.379ex; height:2.843ex;" alt="{\displaystyle \operatorname {hom} (X\times Y,Z)\cong \operatorname {hom} (X(\operatorname {hom} (Y,Z))}" loading="lazy"></span>) the category of sets is a <a href="Closed_monoidal_category" title="Closed monoidal category">closed monoidal category</a> with the <a href="Cartesian_product" title="Cartesian product">Cartesian product</a> of sets as tensor product and the one-point set as tensor unit. In the isomorphisms <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda :1\times X\cong X\cong X\times 1:\rho }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>Ξ»<!-- Ξ» --></mi>
<mo>:</mo>
<mn>1</mn>
<mo>Γ<!-- Γ --></mo>
<mi>X</mi>
<mo>β
<!-- β
--></mo>
<mi>X</mi>
<mo>β
<!-- β
--></mo>
<mi>X</mi>
<mo>Γ<!-- Γ --></mo>
<mn>1</mn>
<mo>:</mo>
<mi>Ο<!-- Ο --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lambda :1\times X\cong X\cong X\times 1:\rho }</annotation>
</semantics>
</math></span><img src="./ecb87f83875d5d9b40159bed2e2a4616e102ef0c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.574ex; height:2.676ex;" alt="{\displaystyle \lambda :1\times X\cong X\cong X\times 1:\rho }" loading="lazy"></span> <a href="Natural_transformation" title="Natural transformation">natural in <span class="texhtml"><i>X</i></span></a>, the left and right unitors are the projections <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{1}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle p_{1}}</annotation>
</semantics>
</math></span><img src="./b9b58f22283ca46dd5da309cc34303b06a797783.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.313ex; height:2.009ex;" alt="{\displaystyle p_{1}}" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle p_{2}}</annotation>
</semantics>
</math></span><img src="./43f1b08d7d69712872e051c2b33fdfa9f5d42319.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.313ex; height:2.009ex;" alt="{\displaystyle p_{2}}" loading="lazy"></span> the <a href="Ordered_pair" title="Ordered pair">ordered pairs</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (*,x)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<mo>β<!-- β --></mo>
<mo>,</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle (*,x)}</annotation>
</semantics>
</math></span><img src="./54d6eac1ea5225dcf442721e58bae62c1b4e89a6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.335ex; height:2.843ex;" alt="{\displaystyle (*,x)}" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x,*)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>β<!-- β --></mo>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle (x,*)}</annotation>
</semantics>
</math></span><img src="./d0a96069b453016fce504537b95c51bfb9b07a64.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.335ex; height:2.843ex;" alt="{\displaystyle (x,*)}" loading="lazy"></span> respectively to the element <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>x</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x}</annotation>
</semantics>
</math></span><img src="./87f9e315fd7e2ba406057a97300593c4802b53e4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" loading="lazy"></span>, where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle *}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo>β<!-- β --></mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle *}</annotation>
</semantics>
</math></span><img src="./8e9972f426d9e07855984f73ee195a21dbc21755.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle *}" loading="lazy"></span> is the unique <a href="Point_(mathematics)" class="mw-redirect" title="Point (mathematics)">point</a> in the one-point set.</li></ul></li></ul>
<p>A function on a <a href="Connected_set" class="mw-redirect" title="Connected set">connected set</a> is <a href="Locally_constant" class="mw-redirect" title="Locally constant">locally constant</a> if and only if it is constant.
</p>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
<style data-mw-deduplicate="TemplateStyles:r1239543626">
/* start https://en.wikipedia.org/ */
.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}
/* end https://en.wikipedia.org/ */
</style><div class="reflist">
<div class="mw-references-wrap"><ol class="references">
<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
/* start https://en.wikipedia.org/ */
.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}
/* end https://en.wikipedia.org/ */
</style><cite id="CITEREFTanton2005" class="citation book cs1">Tanton, James (2005). <a rel="nofollow" class="external text" href="https://archive.org/details/encyclopedia-of-mathematics_202206/page/94/mode/1up?view=theater"><i>Encyclopedia of Mathematics</i></a>. Facts on File, New York. p. 94. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-8160-5124-0</bdi>.</cite></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFDawkins2007" class="citation web cs1">Dawkins, Paul (2007). <a rel="nofollow" class="external text" href="http://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx">"College Algebra"</a>. Lamar University. p. 224<span class="reference-accessdate">. Retrieved <span class="nowrap">January 12,</span> 2014</span>.</cite></span>
</li>
<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFCarterCuevasHollidayMarks2005" class="citation book cs1">Carter, John A.; Cuevas, Gilbert J.; Holliday, Berchie; Marks, Daniel; McClure, Melissa S. (2005). "1". <i>Advanced Mathematical Concepts - Pre-calculus with Applications, Student Edition</i> (1 ed.). Glencoe/McGraw-Hill School Pub Co. p. 22. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0078682278</bdi>.</cite></span>
</li>
<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFYoung2021" class="citation book cs1"><a href="Cynthia_Y._Young" title="Cynthia Y. Young">Young, Cynthia Y.</a> (2021). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=BOBDEAAAQBAJ&pg=PA122"><i>Precalculus</i></a> (3rd ed.). John Wiley & Sons. p. 122. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-119-58294-6</bdi>.</cite></span>
</li>
<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFVarbergPurcellRigdon2007" class="citation book cs1">Varberg, Dale E.; Purcell, Edwin J.; Rigdon, Steven E. (2007). <i>Calculus</i> (9th ed.). <a href="Pearson_Prentice_Hall" class="mw-redirect" title="Pearson Prentice Hall">Pearson Prentice Hall</a>. p. 107. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0131469686</bdi>.</cite></span>
</li>
<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.proofwiki.org/wiki/Zero_Derivative_implies_Constant_Function">"Zero Derivative implies Constant Function"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">January 12,</span> 2014</span>.</cite></span>
</li>
<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFLeinster2011" class="citation arxiv cs1">Leinster, Tom (27 Jun 2011). "An informal introduction to topos theory". <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1012.5647">1012.5647</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/math.CT">math.CT</a>].</cite></span>
</li>
</ol></div></div>
<ul><li>Herrlich, Horst and Strecker, George E., <i>Category Theory</i>, Heldermann Verlag (2007).</li></ul>
<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>
<style data-mw-deduplicate="TemplateStyles:r1290876196">
/* start https://en.wikipedia.org/ */
.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .infobox .side-box{font-size:100%}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}
/* end https://en.wikipedia.org/ */
</style><style data-mw-deduplicate="TemplateStyles:r1237033735">
/* start https://en.wikipedia.org/ */
@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}
/* end https://en.wikipedia.org/ */
</style><div class="side-box side-box-right sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">
/* start https://en.wikipedia.org/ */
.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}
/* end https://en.wikipedia.org/ */
</style>
<div class="side-box-flex">
<div class="side-box-image"><span class="noviewer" typeof="mw:File"></span></div>
<div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Constant_functions" class="extiw external" title="commons:Category:Constant functions">Constant functions</a></span>.</div></div>
</div>
<ul><li><span class="citation mathworld" id="Reference-Mathworld-Constant_Function"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/ConstantFunction.html">"Constant Function"</a>. <i><a href="MathWorld" title="MathWorld">MathWorld</a></i>.</cite></span></li>
<li><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://planetmath.org/ConstantFunction">"Constant function"</a>. <i><a href="PlanetMath" title="PlanetMath">PlanetMath</a></i>.</cite></li></ul>
<div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1236075235">
/* start https://en.wikipedia.org/ */
.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}
/* end https://en.wikipedia.org/ */
</style></div><div role="navigation" class="navbox" aria-labelledby="Polynomials_and_polynomial_functions_and_polynomial_equations142" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Polynomials_and_polynomial_functions_and_polynomial_equations142" style="font-size:114%;margin:0 4em"><a href="Polynomial" title="Polynomial">Polynomials</a> and <a href="Polynomial_function" class="mw-redirect" title="Polynomial function">polynomial functions</a> and <a href="Polynomial_equation" class="mw-redirect" title="Polynomial equation">polynomial equations</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">By <a href="Degree_of_a_polynomial" title="Degree of a polynomial">degree</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Zero_polynomial" class="mw-redirect" title="Zero polynomial">Zero polynomial (degree undefined or β1 or ββ)</a></li>
<li><a href="Linear_function_(calculus)" title="Linear function (calculus)">Linear function (1)</a>
<ul><li><a href="Linear_equation" title="Linear equation">Linear equation</a></li></ul></li>
<li><a href="Quadratic_function" title="Quadratic function">Quadratic function (2)</a>
<ul><li><a href="Quadratic_equation" title="Quadratic equation">Quadratic equation</a></li></ul></li>
<li><a href="Cubic_function" title="Cubic function">Cubic function (3)</a>
<ul><li><a href="Cubic_equation" title="Cubic equation">Cubic equation</a></li></ul></li>
<li><a href="Quartic_function" title="Quartic function">Quartic function (4)</a>
<ul><li><a href="Quartic_equation" title="Quartic equation">Quartic equation</a></li></ul></li>
<li><a href="Quintic_function" title="Quintic function">Quintic function (5)</a></li>
<li><a href="Sextic_equation" title="Sextic equation">Sextic equation (6)</a></li>
<li><a href="Septic_equation" title="Septic equation">Septic equation (7)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By properties</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Univariate_polynomial" class="mw-redirect" title="Univariate polynomial">Univariate</a></li>
<li><a href="Bivariate_polynomial" class="mw-redirect" title="Bivariate polynomial">Bivariate</a></li>
<li><a href="Multivariate_polynomial" class="mw-redirect" title="Multivariate polynomial">Multivariate</a></li>
<li><a href="Monomial" title="Monomial">Monomial</a></li>
<li><a href="Binomial_(polynomial)" title="Binomial (polynomial)">Binomial</a></li>
<li><a href="Trinomial" title="Trinomial">Trinomial</a></li>
<li><a href="Irreducible_polynomial" title="Irreducible polynomial">Irreducible</a></li>
<li><a href="Square-free_polynomial" title="Square-free polynomial">Square-free</a></li>
<li><a href="Homogeneous_polynomial" title="Homogeneous polynomial">Homogeneous</a></li>
<li><a href="Quasi-homogeneous_polynomial" title="Quasi-homogeneous polynomial">Quasi-homogeneous</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Tools and algorithms</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Factorization_of_polynomials" title="Factorization of polynomials">Factorization</a></li>
<li><a href="Polynomial_greatest_common_divisor" title="Polynomial greatest common divisor">Greatest common divisor</a></li>
<li><a href="Polynomial_long_division" title="Polynomial long division">Division</a></li>
<li><a href="Horner's_method" title="Horner's method">Horner's method of evaluation</a></li>
<li><a href="Polynomial_identity_testing" title="Polynomial identity testing">Polynomial identity testing</a></li>
<li><a href="Polynomial_resultant" class="mw-redirect" title="Polynomial resultant">Resultant</a></li>
<li><a href="Discriminant" title="Discriminant">Discriminant</a></li>
<li><a href="Gr%C3%B6bner_basis" title="GrΓΆbner basis">GrΓΆbner basis</a></li></ul>
</div></td></tr></tbody></table></div>
<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Function330" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Function330" style="font-size:114%;margin:0 4em"><a href="Function_(mathematics)" title="Function (mathematics)">Function</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>
<ul><li><a href="History_of_the_function_concept" title="History of the function concept">History</a></li>
<li><a href="List_of_mathematical_functions" title="List of mathematical functions">List of specific functions</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types by domain and codomain</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Boolean-valued_function" title="Boolean-valued function"><span class="texhtml">X β πΉ</span></a></li>
<li><a href="Ordered_pair" title="Ordered pair"><span class="texhtml">πΉ β X</span></a></li>
<li><a href="Boolean_function" title="Boolean function"><span class="texhtml">πΉβΏ β X</span></a></li>
<li><a href="Integer-valued_function" title="Integer-valued function"><span class="texhtml">X β β€</span></a></li>
<li><a href="Sequence" title="Sequence"><span class="texhtml">β€ β X</span></a></li>
<li><a href="Real-valued_function" title="Real-valued function"><span class="texhtml">X β β</span></a></li>
<li><a href="Function_of_a_real_variable" title="Function of a real variable"><span class="texhtml">β β X</span></a></li>
<li><a href="Function_of_several_real_variables" title="Function of several real variables"><span class="texhtml">ββΏ β X</span></a></li>
<li><a href="Complex-valued_function" class="mw-redirect" title="Complex-valued function"><span class="texhtml">X β β</span></a></li>
<li><a href="Function_of_a_complex_variable" class="mw-redirect" title="Function of a complex variable"><span class="texhtml">β β X</span></a></li>
<li><a href="Function_of_several_complex_variables" title="Function of several complex variables"><span class="texhtml">ββΏ β X</span></a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Classes/properties</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul>
<li><a href="Identity_function" title="Identity function">Identity</a></li>
<li><a href="Linear_map" title="Linear map">Linear</a></li>
<li><a href="Polynomial" title="Polynomial">Polynomial</a></li>
<li><a href="Rational_function" title="Rational function">Rational</a></li>
<li><a href="Algebraic_function" title="Algebraic function">Algebraic</a></li>
<li><a href="Analytic_function" title="Analytic function">Analytic</a></li>
<li><a href="Smooth_function" class="mw-redirect" title="Smooth function">Smooth</a></li>
<li><a href="Continuous_function" title="Continuous function">Continuous</a></li>
<li><a href="Measurable_function" title="Measurable function">Measurable</a></li>
<li><a href="Injective_function" title="Injective function">Injective</a></li>
<li><a href="Surjective_function" title="Surjective function">Surjective</a></li>
<li><a href="Bijection" title="Bijection">Bijective</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Constructions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Restriction_(mathematics)" title="Restriction (mathematics)">Restriction</a></li>
<li><a href="Function_composition" title="Function composition">Composition</a></li>
<li><a href="Lambda_calculus" title="Lambda calculus">Ξ»</a></li>
<li><a href="Inverse_function" title="Inverse function">Inverse</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Generalizations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Relation_(mathematics)" title="Relation (mathematics)">Relation</a> (<a href="Binary_relation" title="Binary relation">Binary relation</a>)</li>
<li><a href="Set-valued_function" title="Set-valued function">Set-valued</a></li>
<li><a href="Multivalued_function" title="Multivalued function">Multivalued</a></li>
<li><a href="Partial_function" title="Partial function">Partial</a></li>
<li><a href="Implicit_function" title="Implicit function">Implicit</a></li>
<li><a href="Function_space" title="Function space">Space</a></li>
<li><a href="Higher-order_function" title="Higher-order function">Higher-order</a></li>
<li><a href="Morphism" title="Morphism">Morphism</a></li>
<li><a href="Functor" title="Functor">Functor</a></li></ul>
</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>
<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Category</li></ul>
</div></td></tr></tbody></table></div></div><!--htdig_noindex--><div><div class="zim-footer">
This article is issued from <a class="external text" title="Last edited on 2024-12-05" href="https://en.wikipedia.org/wiki/?title=Constant_function&oldid=1261268451">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.
</div>
</div><!--/htdig_noindex--></div>
</div>
</main>
</div>
</div>
</div>
</body></html>