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(From these references no 0018 text was directly copied.) 0019 0020 Copyright 2007, 2008, 2009, 2010, 2011, 2012, 2013, 0021 2014, 2015, 2016, 2017, 2018 Karl Berry. 0022 0023 Copyright 1988, 1994, 2007 Stephen Gilmore. 0024 0025 Copyright 1994, 1995, 1996 Torsten Martinsen. 0026 0027 Permission is granted to make and distribute verbatim copies of 0028 this manual provided the copyright notice and this permission notice 0029 are preserved on all copies. 0030 0031 0032 Permission is granted to copy and distribute modified versions of this 0033 manual under the conditions for verbatim copying, provided that the entire 0034 resulting derived work is distributed under the terms of a permission 0035 notice identical to this one. 0036 0037 Permission is granted to copy and distribute translations of this manual 0038 into another language, under the above conditions for modified versions. --> 0039 <!-- Created by GNU Texinfo 6.5, http://www.gnu.org/software/texinfo/ --> 0040 <head> 0041 <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> 0042 <title>Dots (LaTeX2e unofficial reference manual (November 2018))</title> 0043 0044 <meta name="description" content="Dots (LaTeX2e unofficial reference manual (November 2018))"> 0045 <meta name="keywords" content="Dots (LaTeX2e unofficial reference manual (November 2018))"> 0046 <meta name="resource-type" content="document"> 0047 <meta name="distribution" content="global"> 0048 <meta name="Generator" content="makeinfo"> 0049 <link href="index.html#Top" rel="start" title="Top"> 0050 <link href="IndexDocument.html#Index" rel="index" title="Index"> 0051 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> 0052 <link href="Math-symbols.html#Math-symbols" rel="up" title="Math symbols"> 0053 <link href="Greek-letters.html#Greek-letters" rel="next" title="Greek letters"> 0054 <link href="_005cbigl-_0026-_005cbigr-etc.html#g_t_005cbigl-_0026-_005cbigr-etc" rel="prev" title="\bigl & \bigr etc"> 0055 <style type="text/css"> 0056 <!-- 0057 /* $Id: latex2e.css 690 2018-09-15 15:20:19Z jimhefferon $ 0058 Minor css for latexrefman. Public domain. 0059 Originally written by Jim Hefferon and Karl Berry, 2018. */ 0060 0061 /* So you can style for yourself */ 0062 @import url("/css/latexreflocal.css"); 0063 0064 0065 0066 a.summary-letter {text-decoration: none} 0067 blockquote.indentedblock {margin-right: 0em} 0068 blockquote.smallindentedblock {margin-right: 0em; font-size: smaller} 0069 blockquote.smallquotation {font-size: smaller} 0070 div.display {margin-left: 3.2em} 0071 div.example {margin-left: 3.2em} 0072 div.lisp {margin-left: 3.2em} 0073 div.smalldisplay {margin-left: 3.2em} 0074 div.smallexample {margin-left: 3.2em} 0075 div.smalllisp {margin-left: 3.2em} 0076 kbd {font-style: oblique} 0077 pre.display {font-family: inherit} 0078 pre.format {font-family: inherit} 0079 pre.menu-comment {font-family: serif} 0080 pre.menu-preformatted {font-family: serif} 0081 pre.smalldisplay {font-family: inherit; font-size: smaller} 0082 pre.smallexample {font-size: smaller} 0083 pre.smallformat {font-family: inherit; font-size: smaller} 0084 pre.smalllisp {font-size: smaller} 0085 span.nolinebreak {white-space: nowrap} 0086 span.roman {font-family: initial; font-weight: normal} 0087 span.sansserif {font-family: sans-serif; font-weight: normal} 0088 ul.no-bullet {list-style: none} 0089 BODY { 0090 margin-top: 1em; 0091 margin-left: 1em; /* auto results in two-digit <ol> lost off left */ 0092 margin-right: 1em; 0093 margin-bottom: 1em; 0094 /* the idea is to use the whole window, unless it is ridiculously 0095 wide, probably with too-small fonts, too. */ 0096 max-width: 64em; 0097 } 0098 0099 /* Because we want @math{... @code ...} to be upright, not slanted, 0100 and Texinfo won't fix it. */ 0101 code {font-style:normal; font-family:monospace; } 0102 0103 /* We put a link to our own home page at the bottom. */ 0104 div.referenceinfo {font-size:small;} 0105 0106 --> 0107 </style> 0108 0109 0110 </head> 0111 0112 <body lang="en"> 0113 <a name="Dots"></a> 0114 <div class="header"> 0115 <p> 0116 Next: <a href="Greek-letters.html#Greek-letters" accesskey="n" rel="next">Greek letters</a>, Previous: <a href="Delimiters.html#Delimiters" accesskey="p" rel="prev">Delimiters</a>, Up: <a href="Math-symbols.html#Math-symbols" accesskey="u" rel="up">Math symbols</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="IndexDocument.html#Index" title="Index" rel="index">Index</a>]</p> 0117 </div> 0118 <hr> 0119 <a name="Dots_002c-horizontal-or-vertical"></a> 0120 <h4 class="subsection">16.2.6 Dots, horizontal or vertical</h4> 0121 0122 <a name="index-ellipses"></a> 0123 <a name="index-dots"></a> 0124 0125 <p>Ellipses are the three dots (usually three) indicating that a pattern 0126 continues. 0127 </p> 0128 <div class="example"> 0129 <pre class="example">\begin{array}{cccc} 0130 a_{0,0} &a_{0,1} &a_{0,2} &\ldots \\ 0131 a_{1,0} &\ddots \\ 0132 \vdots 0133 \end{array} 0134 </pre></div> 0135 0136 <p>LaTeX provides these. 0137 </p> 0138 <dl compact="compact"> 0139 <dd><a name="ellipses-cdots"></a></dd> 0140 <dt><code>\cdots</code> 0141 <a name="index-_005ccdots"></a> 0142 </dt> 0143 <dd><p>Horizontal ellipsis with the dots raised to the center of the line, as 0144 in ⋯. Used as: <code>\( a_0\cdot a_1\cdots a_{n-1} 0145 \)</code>. 0146 </p> 0147 <a name="ellipses-ddots"></a></dd> 0148 <dt><code>\ddots</code> 0149 <a name="index-_005cddots"></a> 0150 </dt> 0151 <dd><p>Diagonal ellipsis, ⋱. See the above array example for a 0152 usage. 0153 </p> 0154 <a name="ellipses-ldots"></a></dd> 0155 <dt><code>\ldots</code> 0156 <a name="index-_005cldots"></a> 0157 </dt> 0158 <dd><p>Ellipsis on the baseline, …. Used as: <code>\( 0159 x_0,\ldots x_{n-1} \)</code>. Another example is the above array example. A 0160 synonym is <code>\mathellipsis</code>. A synonym from the <samp>amsmath</samp> 0161 package is <code>\hdots</code>. 0162 </p> 0163 <p>You can also use this command outside of mathematical text, as in 0164 <code>The gears, brakes, \ldots{} are all broken</code>. (In a paragraph 0165 mode or LR mode a synonym for <code>\ldots</code> is <code>\dots</code>.) 0166 </p> 0167 <a name="ellipses-vdots"></a></dd> 0168 <dt><code>\vdots</code> 0169 <a name="index-_005cvdots"></a> 0170 </dt> 0171 <dd><p>Vertical ellipsis, ⋮. See the above array example for a 0172 usage. 0173 </p> 0174 </dd> 0175 </dl> 0176 0177 <a name="index-package_002c-amsmath-8"></a> 0178 <a name="index-amsmath-package-8"></a> 0179 0180 <p>The <samp>amsmath</samp> package has the command <code>\dots</code> to semantically 0181 mark up ellipses. This example produces two different-looking outputs 0182 for the first two uses of the <code>\dots</code> command. 0183 </p> 0184 <div class="example"> 0185 <pre class="example">\usepackage{amsmath} % in preamble 0186 ... 0187 Suppose that \( p_0, p_1, \dots, p_{n-1} \) lists all of the primes. 0188 Observe that \( p_0\cdot p_1 \dots \cdot p_{n-1} +1 \) is not a 0189 multiple of any \( p_i \). 0190 Conclusion: there are infinitely many primes \( p_0, p_1, \dotsc \). 0191 </pre></div> 0192 0193 <p>In the first line LaTeX looks to the comma following <code>\dots</code> to 0194 determine that it should output an ellipsis on the baseline. The second 0195 line has a <code>\cdot</code> following <code>\dots</code> so LaTeX outputs an 0196 ellipsis that is on the math axis, vertically centered. However, the 0197 third usage has no follow-on character so you have to tell LaTeX what 0198 to do. You can use one of the commands: <code>\dotsc</code> if you need the 0199 ellipsis appropriate for a comma following, <code>\dotsb</code> if you need 0200 the ellipses that fits when the dots are followed by a binary operator 0201 or relation symbol, <code>\dotsi</code> for dots with integrals, or 0202 <code>\dotso</code> for others. 0203 </p> 0204 0205 0206 0207 <hr/><div class='referenceinfo'> <a href='https://latexref.xyz/'> <i>Unofficial LaTeX2e reference manual</i></a></div> 0208 </body> 0209 </html>