File indexing completed on 2024-11-24 04:34:44
0001 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> 0002 <html> 0003 <!-- This document is an unofficial reference manual for LaTeX, a 0004 document preparation system, version of November 2018. 0005 0006 This manual was originally translated from LATEX.HLP v1.0a in the 0007 VMS Help Library. The pre-translation version was written by 0008 George D. Greenwade of Sam Houston State University. The 0009 LaTeX 2.09 version was written by Stephen Gilmore. The 0010 LaTeX2e version was adapted from this by Torsten Martinsen. Karl 0011 Berry made further updates and additions, and gratefully acknowledges 0012 using Hypertext Help with LaTeX, by Sheldon Green, and 0013 LaTeX Command Summary (for LaTeX 2.09) by 0014 L. Botway and C. Biemesderfer (published by the TeX Users 0015 Group as TeXniques number 10), as reference material. We also 0016 gratefully acknowledge additional material appearing in 0017 latex2e-reference by Martin Herbert Dietze. (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>Math symbols (LaTeX2e unofficial reference manual (November 2018))</title> 0043 0044 <meta name="description" content="Math symbols (LaTeX2e unofficial reference manual (November 2018))"> 0045 <meta name="keywords" content="Math symbols (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-formulas.html#Math-formulas" rel="up" title="Math formulas"> 0053 <link href="Arrows.html#Arrows" rel="next" title="Arrows"> 0054 <link href="Subscripts-_0026-superscripts.html#Subscripts-_0026-superscripts" rel="prev" title="Subscripts & superscripts"> 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="Math-symbols"></a> 0114 <div class="header"> 0115 <p> 0116 Next: <a href="Math-functions.html#Math-functions" accesskey="n" rel="next">Math functions</a>, Previous: <a href="Subscripts-_0026-superscripts.html#Subscripts-_0026-superscripts" accesskey="p" rel="prev">Subscripts & superscripts</a>, Up: <a href="Math-formulas.html#Math-formulas" accesskey="u" rel="up">Math formulas</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="Math-symbols-1"></a> 0120 <h3 class="section">16.2 Math symbols</h3> 0121 0122 <a name="index-math-symbols"></a> 0123 <a name="index-symbols_002c-math"></a> 0124 <a name="index-greek-letters"></a> 0125 0126 <a name="index-package_002c-comprehensive"></a> 0127 <a name="index-comprehensive-package"></a> 0128 0129 0130 <p>LaTeX provides almost any mathematical or technical symbol that 0131 anyone uses. For example, if you include <code>$\pi$</code> in your source, 0132 you will get the pi symbol π. See the “Comprehensive 0133 LaTeX Symbol List” package at 0134 <a href="https://ctan.org/pkg/comprehensive">https://ctan.org/pkg/comprehensive</a>. 0135 </p> 0136 <p>Here is a list of commonly-used symbols. It is by no means exhaustive. 0137 Each symbol is described with a short phrase, and its symbol class, 0138 which determines the spacing around it, is given in parenthesis. Unless 0139 said otherwise, the commands for these symbols can be used only in math 0140 mode. To redefine a command so that it can be used whatever the current 0141 mode, see <a href="_005censuremath.html#g_t_005censuremath">\ensuremath</a>. 0142 </p> 0143 0144 <dl compact="compact"> 0145 <dt><code>\|</code> 0146 <a name="index-_005c_007c"></a> 0147 </dt> 0148 <dd><p>∥ Parallel (relation). Synonym: <code>\parallel</code>. 0149 </p> 0150 </dd> 0151 <dt><code>\aleph</code> 0152 <a name="index-_005caleph"></a> 0153 </dt> 0154 <dd><p>ℵ Aleph, transfinite cardinal (ordinary). 0155 </p> 0156 </dd> 0157 <dt><code>\alpha</code> 0158 <a name="index-_005calpha"></a> 0159 </dt> 0160 <dd><p>α Lowercase Greek letter alpha (ordinary). 0161 </p> 0162 </dd> 0163 <dt><code>\amalg</code> 0164 <a name="index-_005camalg"></a> 0165 </dt> 0166 <dd><p>⨿ Disjoint union (binary) 0167 </p> 0168 </dd> 0169 <dt><code>\angle</code> 0170 <a name="index-_005cangle"></a> 0171 </dt> 0172 <dd><p>∠ Geometric angle (ordinary). Similar: less-than 0173 sign <code><</code> and angle bracket <code>\langle</code>. 0174 </p> 0175 </dd> 0176 <dt><code>\approx</code> 0177 <a name="index-_005capprox"></a> 0178 </dt> 0179 <dd><p>≈ Almost equal to (relation). 0180 </p> 0181 </dd> 0182 <dt><code>\ast</code> 0183 <a name="index-_005cast"></a> 0184 </dt> 0185 <dd><p>∗ Asterisk operator, convolution, six-pointed 0186 (binary). Synonym: <code>*</code>, which is often a superscript or 0187 subscript, as in the Kleene star. Similar: <code>\star</code>, which is 0188 five-pointed, and is sometimes used as a general binary operation, and 0189 sometimes reserved for cross-correlation. 0190 </p> 0191 </dd> 0192 <dt><code>\asymp</code> 0193 <a name="index-_005casymp"></a> 0194 </dt> 0195 <dd><p>≍ Asymptotically equivalent (relation). 0196 </p> 0197 </dd> 0198 <dt><code>\backslash</code> 0199 <a name="index-_005cbackslash"></a> 0200 </dt> 0201 <dd><p>\ Backslash (ordinary). Similar: set minus <code>\setminus</code>, and 0202 <code>\textbackslash</code> for backslash outside of math mode. 0203 </p> 0204 </dd> 0205 <dt><code>\beta</code> 0206 <a name="index-_005cbeta"></a> 0207 </dt> 0208 <dd><p>β Lowercase Greek letter beta (ordinary). 0209 </p> 0210 </dd> 0211 <dt><code>\bigcap</code> 0212 <a name="index-_005cbigcap"></a> 0213 </dt> 0214 <dd><p>⋂ Variable-sized, or n-ary, intersection (operator). Similar: 0215 binary intersection <code>\cap</code>. 0216 </p> 0217 </dd> 0218 <dt><code>\bigcirc</code> 0219 <a name="index-_005cbigcirc"></a> 0220 </dt> 0221 <dd><p>⚪ Circle, larger (binary). Similar: function 0222 composition <code>\circ</code>. 0223 </p> 0224 </dd> 0225 <dt><code>\bigcup</code> 0226 <a name="index-_005cbigcup"></a> 0227 </dt> 0228 <dd><p>⋃ Variable-sized, or n-ary, union (operator). Similar: binary 0229 union <code>\cup</code>. 0230 </p> 0231 </dd> 0232 <dt><code>\bigodot</code> 0233 <a name="index-_005cbigodot"></a> 0234 </dt> 0235 <dd><p>⨀ Variable-sized, or n-ary, circled dot operator (operator). 0236 </p> 0237 </dd> 0238 <dt><code>\bigoplus</code> 0239 <a name="index-_005cbigoplus"></a> 0240 </dt> 0241 <dd><p>⨁ Variable-sized, or n-ary, circled plus operator (operator). 0242 </p> 0243 </dd> 0244 <dt><code>\bigotimes</code> 0245 <a name="index-_005cbigotimes"></a> 0246 </dt> 0247 <dd><p>⨂ Variable-sized, or n-ary, circled times operator (operator). 0248 </p> 0249 </dd> 0250 <dt><code>\bigtriangledown</code> 0251 <a name="index-_005cbigtriangledown"></a> 0252 </dt> 0253 <dd><p>▽ Variable-sized, or n-ary, open triangle pointing down 0254 (operator). 0255 </p> 0256 </dd> 0257 <dt><code>\bigtriangleup</code> 0258 <a name="index-_005cbigtriangleup"></a> 0259 </dt> 0260 <dd><p>△ Variable-sized, or n-ary, open triangle pointing up (operator). 0261 </p> 0262 </dd> 0263 <dt><code>\bigsqcup</code> 0264 <a name="index-_005cbigsqcup"></a> 0265 </dt> 0266 <dd><p>⨆ Variable-sized, or n-ary, square union (operator). 0267 </p> 0268 </dd> 0269 <dt><code>\biguplus</code> 0270 <a name="index-_005cbiguplus"></a> 0271 </dt> 0272 <dd><p>⨄ Variable-sized, or n-ary, union operator with a plus 0273 (operator). (Note that the name has only one p.) 0274 </p> 0275 </dd> 0276 <dt><code>\bigvee</code> 0277 <a name="index-_005cbigvee"></a> 0278 </dt> 0279 <dd><p>⋁ Variable-sized, or n-ary, logical-and (operator). 0280 </p> 0281 </dd> 0282 <dt><code>\bigwedge</code> 0283 <a name="index-_005cbigwedge"></a> 0284 </dt> 0285 <dd><p>⋀ Variable-sized, or n-ary, logical-or (operator). 0286 </p> 0287 </dd> 0288 <dt><code>\bot</code> 0289 <a name="index-_005cbot"></a> 0290 </dt> 0291 <dd><p>⊥ Up tack, bottom, least element of a partially ordered 0292 set, or a contradiction (ordinary). See also <code>\top</code>. 0293 </p> 0294 </dd> 0295 <dt><code>\bowtie</code> 0296 <a name="index-_005cbowtie"></a> 0297 </dt> 0298 <dd><p>⋈ Natural join of two relations (relation). 0299 </p> 0300 </dd> 0301 <dt><code>\Box</code> 0302 <a name="index-_005cBox"></a> 0303 </dt> 0304 <dd><p>□ Modal operator for necessity; square open box 0305 (ordinary). Not available in plain TeX. In LaTeX you need to load the <samp>amssymb</samp> package. 0306 </p> 0307 </dd> 0308 <dt><code>\bullet</code> 0309 <a name="index-_005cbullet"></a> 0310 </dt> 0311 <dd><a name="index-bullet-symbol"></a> 0312 <p>• Bullet (binary). Similar: multiplication 0313 dot <code>\cdot</code>. 0314 </p> 0315 </dd> 0316 <dt><code>\cap</code> 0317 <a name="index-_005ccap"></a> 0318 </dt> 0319 <dd><p>∩ Intersection of two sets (binary). Similar: variable-sized 0320 operator <code>\bigcap</code>. 0321 </p> 0322 </dd> 0323 <dt><code>\cdot</code> 0324 <a name="index-_005ccdot"></a> 0325 </dt> 0326 <dd><p>⋅ Multiplication (binary). Similar: Bullet 0327 dot <code>\bullet</code>. 0328 </p> 0329 </dd> 0330 <dt><code>\chi</code> 0331 <a name="index-_005cchi"></a> 0332 </dt> 0333 <dd><p>χ Lowercase Greek chi (ordinary). 0334 </p> 0335 </dd> 0336 <dt><code>\circ</code> 0337 <a name="index-_005ccirc"></a> 0338 </dt> 0339 <dd><p>∘ Function composition, ring operator (binary). Similar: 0340 variable-sized operator <code>\bigcirc</code>. 0341 </p> 0342 </dd> 0343 <dt><code>\clubsuit</code> 0344 <a name="index-_005cclubsuit"></a> 0345 </dt> 0346 <dd><p>♣ Club card suit (ordinary). 0347 </p> 0348 </dd> 0349 <dt><code>\complement</code> 0350 <a name="index-_005ccomplement"></a> 0351 </dt> 0352 <dd><p>∁ Set complement, used as a superscript as in 0353 <code>$S^\complement$</code> (ordinary). Not available in plain TeX. In LaTeX you need to load the <samp>amssymb</samp> package. Also used: 0354 <code>$S^{\mathsf{c}}$</code> or <code>$\bar{S}$</code>. 0355 </p> 0356 </dd> 0357 <dt><code>\cong</code> 0358 <a name="index-_005ccong"></a> 0359 </dt> 0360 <dd><p>≅ Congruent (relation). 0361 </p> 0362 </dd> 0363 <dt><code>\coprod</code> 0364 <a name="index-_005ccoprod"></a> 0365 </dt> 0366 <dd><p>∐ Coproduct (operator). 0367 </p> 0368 </dd> 0369 <dt><code>\cup</code> 0370 <a name="index-_005ccup"></a> 0371 </dt> 0372 <dd><p>∪ Union of two sets (binary). Similar: variable-sized 0373 operator <code>\bigcup</code>. 0374 </p> 0375 </dd> 0376 <dt><code>\dagger</code> 0377 <a name="index-_005cdagger"></a> 0378 </dt> 0379 <dd><p>† Dagger relation (binary). 0380 </p> 0381 </dd> 0382 <dt><code>\dashv</code> 0383 <a name="index-_005cdashv"></a> 0384 </dt> 0385 <dd><p>⊣ Dash with vertical, reversed turnstile (relation). Similar: 0386 turnstile <code>\vdash</code>. 0387 </p> 0388 </dd> 0389 <dt><code>\ddagger</code> 0390 <a name="index-_005cddagger"></a> 0391 </dt> 0392 <dd><p>‡ Double dagger relation (binary). 0393 </p> 0394 </dd> 0395 <dt><code>\Delta</code> 0396 <a name="index-_005cDelta"></a> 0397 </dt> 0398 <dd><p>Δ Greek uppercase delta, used for increment (ordinary). 0399 </p> 0400 </dd> 0401 <dt><code>\delta</code> 0402 <a name="index-_005cdelta"></a> 0403 </dt> 0404 <dd><p>δ Greek lowercase delta (ordinary). 0405 </p> 0406 </dd> 0407 <dt><code>\Diamond</code> 0408 <a name="index-_005cDiamond"></a> 0409 </dt> 0410 <dd><p>◇ Large diamond operator (ordinary). Not available in plain TeX. In LaTeX you need to load the <samp>amssymb</samp> package. 0411 </p> 0412 </dd> 0413 <dt><code>\diamond</code> 0414 <a name="index-_005cdiamond"></a> 0415 </dt> 0416 <dd><p>⋄ Diamond operator (binary). Similar: large 0417 diamond <code>\Diamond</code>, circle bullet <code>\bullet</code>. 0418 </p> 0419 </dd> 0420 <dt><code>\diamondsuit</code> 0421 <a name="index-_005cdiamondsuit"></a> 0422 </dt> 0423 <dd><p>♢ Diamond card suit (ordinary). 0424 </p> 0425 </dd> 0426 <dt><code>\div</code> 0427 <a name="index-_005cdiv"></a> 0428 </dt> 0429 <dd><p>÷ Division sign (binary). 0430 </p> 0431 </dd> 0432 <dt><code>\doteq</code> 0433 <a name="index-_005cdoteq"></a> 0434 </dt> 0435 <dd><p>≐ Approaches the limit (relation). Similar: geometrically equal 0436 to <code>\Doteq</code>. 0437 </p> 0438 </dd> 0439 <dt><code>\downarrow</code> 0440 <a name="index-_005cdownarrow"></a> 0441 </dt> 0442 <dd><p>↓ Down arrow, converges (relation). Similar: 0443 <code>\Downarrow</code> double line down arrow. 0444 </p> 0445 </dd> 0446 <dt><code>\Downarrow</code> 0447 <a name="index-_005cDownarrow"></a> 0448 </dt> 0449 <dd><p>⇓ Double line down arrow (relation). Similar: 0450 <code>\downarrow</code> single line down arrow. 0451 </p> 0452 </dd> 0453 <dt><code>\ell</code> 0454 <a name="index-_005cell"></a> 0455 </dt> 0456 <dd><p>ℓ Lowercase cursive letter l (ordinary). 0457 </p> 0458 </dd> 0459 <dt><code>\emptyset</code> 0460 <a name="index-_005cemptyset"></a> 0461 </dt> 0462 <dd><p>∅ Empty set symbol (ordinary). The variant form is 0463 <code>\varnothing</code>. 0464 </p> 0465 </dd> 0466 <dt><code>\epsilon</code> 0467 <a name="index-_005cepsilon"></a> 0468 </dt> 0469 <dd><p>ϵ Lowercase lunate epsilon (ordinary). Similar to 0470 Greek text letter. More widely used in mathematics is the script small 0471 letter epsilon <code>\varepsilon</code> ε. Related: 0472 the set membership relation <code>\in</code> ∈. 0473 </p> 0474 </dd> 0475 <dt><code>\equiv</code> 0476 <a name="index-_005cequiv"></a> 0477 </dt> 0478 <dd><p>≡ Equivalence (relation). 0479 </p> 0480 </dd> 0481 <dt><code>\eta</code> 0482 <a name="index-_005ceta"></a> 0483 </dt> 0484 <dd><p>η Lowercase Greek letter (ordinary). 0485 </p> 0486 </dd> 0487 <dt><code>\exists</code> 0488 <a name="index-_005cexists"></a> 0489 </dt> 0490 <dd><p>∃ Existential quantifier (ordinary). 0491 </p> 0492 </dd> 0493 <dt><code>\flat</code> 0494 <a name="index-_005cflat"></a> 0495 </dt> 0496 <dd><p>♭ Musical flat (ordinary). 0497 </p> 0498 </dd> 0499 <dt><code>\forall</code> 0500 <a name="index-_005cforall"></a> 0501 </dt> 0502 <dd><p>∀ Universal quantifier (ordinary). 0503 </p> 0504 </dd> 0505 <dt><code>\frown</code> 0506 <a name="index-_005cfrown"></a> 0507 </dt> 0508 <dd><p>⌢ Downward curving arc (ordinary). 0509 </p> 0510 </dd> 0511 <dt><code>\Gamma</code> 0512 <a name="index-_005cGamma"></a> 0513 </dt> 0514 <dd><p>Γ uppercase Greek letter (ordinary). 0515 </p> 0516 </dd> 0517 <dt><code>\gamma</code> 0518 <a name="index-_005cgamma"></a> 0519 </dt> 0520 <dd><p>γ Lowercase Greek letter (ordinary). 0521 </p> 0522 </dd> 0523 <dt><code>\ge</code> 0524 <a name="index-_005cge"></a> 0525 </dt> 0526 <dd><p>≥ Greater than or equal to (relation). This is a synonym 0527 for <code>\geq</code>. 0528 </p> 0529 </dd> 0530 <dt><code>\geq</code> 0531 <a name="index-_005cgeq"></a> 0532 </dt> 0533 <dd><p>≥ Greater than or equal to (relation). This is a synonym 0534 for <code>\ge</code>. 0535 </p> 0536 </dd> 0537 <dt><code>\gets</code> 0538 <a name="index-_005cgets"></a> 0539 </dt> 0540 <dd><p>← Is assigned the value (relation). 0541 Synonym: <code>\leftarrow</code>. 0542 </p> 0543 </dd> 0544 <dt><code>\gg</code> 0545 <a name="index-_005cgg"></a> 0546 </dt> 0547 <dd><p>≫ Much greater than (relation). Similar: much less 0548 than <code>\ll</code>. 0549 </p> 0550 </dd> 0551 <dt><code>\hbar</code> 0552 <a name="index-_005chbar"></a> 0553 </dt> 0554 <dd><p>ℏ Planck constant over two pi (ordinary). 0555 </p> 0556 </dd> 0557 <dt><code>\heartsuit</code> 0558 <a name="index-_005cheartsuit"></a> 0559 </dt> 0560 <dd><p>♡ Heart card suit (ordinary). 0561 </p> 0562 </dd> 0563 <dt><code>\hookleftarrow</code> 0564 <a name="index-_005chookleftarrow"></a> 0565 </dt> 0566 <dd><p>↩ Hooked left arrow (relation). 0567 </p> 0568 </dd> 0569 <dt><code>\hookrightarrow</code> 0570 <a name="index-_005chookrightarrow"></a> 0571 </dt> 0572 <dd><p>↪ Hooked right arrow (relation). 0573 </p> 0574 </dd> 0575 <dt><code>\iff</code> 0576 <a name="index-_005ciff"></a> 0577 </dt> 0578 <dd><p>⟷ If and only if (relation). It is <code>\Longleftrightarrow</code> 0579 with a <code>\thickmuskip</code> on either side. 0580 </p> 0581 </dd> 0582 <dt><code>\Im</code> 0583 <a name="index-_005cIm"></a> 0584 </dt> 0585 <dd><p>ℑ Imaginary part (ordinary). See: real part <code>\Re</code>. 0586 </p> 0587 </dd> 0588 <dt><code>\imath</code> 0589 <a name="index-_005cimath"></a> 0590 </dt> 0591 <dd><a name="index-dotless-i_002c-math"></a> 0592 <p>Dotless i; used when you are putting an accent on an i (see <a href="Math-accents.html#Math-accents">Math accents</a>). 0593 </p> 0594 </dd> 0595 <dt><code>\in</code> 0596 <a name="index-_005cin"></a> 0597 </dt> 0598 <dd><p>∈ Set element (relation). See also: lowercase lunate 0599 epsilon <code>\epsilon</code>ϵ and small letter script 0600 epsilon <code>\varepsilon</code>. 0601 </p> 0602 </dd> 0603 <dt><code>\infty</code> 0604 <a name="index-_005cinfty"></a> 0605 </dt> 0606 <dd><p>∞ Infinity (ordinary). 0607 </p> 0608 </dd> 0609 <dt><code>\int</code> 0610 <a name="index-_005cint"></a> 0611 </dt> 0612 <dd><p>∫ Integral (operator). 0613 </p> 0614 </dd> 0615 <dt><code>\iota</code> 0616 <a name="index-_005ciota"></a> 0617 </dt> 0618 <dd><p>ι Lowercase Greek letter (ordinary). 0619 </p> 0620 </dd> 0621 <dt><code>\Join</code> 0622 <a name="index-_005cJoin"></a> 0623 </dt> 0624 <dd><p>⨝ Condensed bowtie symbol (relation). Not available in Plain 0625 TeX. 0626 </p> 0627 </dd> 0628 <dt><code>\jmath</code> 0629 <a name="index-_005cjmath"></a> 0630 </dt> 0631 <dd><a name="index-dotless-j_002c-math"></a> 0632 <p>Dotless j; used when you are putting an accent on a j (see <a href="Math-accents.html#Math-accents">Math accents</a>). 0633 </p> 0634 </dd> 0635 <dt><code>\kappa</code> 0636 <a name="index-_005ckappa"></a> 0637 </dt> 0638 <dd><p>κ Lowercase Greek letter (ordinary). 0639 </p> 0640 </dd> 0641 <dt><code>\Lambda</code> 0642 <a name="index-_005cLambda"></a> 0643 </dt> 0644 <dd><p>Λ uppercase Greek letter (ordinary). 0645 </p> 0646 </dd> 0647 <dt><code>\lambda</code> 0648 <a name="index-_005clambda"></a> 0649 </dt> 0650 <dd><p>λ Lowercase Greek letter (ordinary). 0651 </p> 0652 </dd> 0653 <dt><code>\land</code> 0654 <a name="index-_005cland"></a> 0655 </dt> 0656 <dd><p>∧ Logical and (binary). This is a synonym for <code>\wedge</code>. 0657 See also logical or <code>\lor</code>. 0658 </p> 0659 </dd> 0660 <dt><code>\langle</code> 0661 <a name="index-_005clangle"></a> 0662 </dt> 0663 <dd><p>⟨ Left angle, or sequence, bracket (opening). Similar: 0664 less-than <code><</code>. Matches <code>\rangle</code>. 0665 </p> 0666 </dd> 0667 <dt><code>\lbrace</code> 0668 <a name="index-_005clbrace"></a> 0669 </dt> 0670 <dd><p>{ Left curly brace 0671 (opening). Synonym: <code>\{</code>. Matches <code>\rbrace</code>. 0672 </p> 0673 </dd> 0674 <dt><code>\lbrack</code> 0675 <a name="index-_005clbrack"></a> 0676 </dt> 0677 <dd><p>[ Left square bracket (opening). 0678 Synonym: <code>[</code>. Matches <code>\rbrack</code>. 0679 </p> 0680 </dd> 0681 <dt><code>\lceil</code> 0682 <a name="index-_005clceil"></a> 0683 </dt> 0684 <dd><p>⌈ Left ceiling bracket, like a square bracket but with the bottom 0685 shaved off (opening). Matches <code>\rceil</code>. 0686 </p> 0687 </dd> 0688 <dt><code>\le</code> 0689 <a name="index-_005cle"></a> 0690 </dt> 0691 <dd><p>≤ Less than or equal to (relation). This is a synonym 0692 for <code>\leq</code>. 0693 </p> 0694 </dd> 0695 <dt><code>\leadsto</code> 0696 <a name="index-_005cleadsto"></a> 0697 </dt> 0698 <dd><p>⇝ Squiggly right arrow (relation). 0699 To get this symbol outside of math mode you can put 0700 <code>\newcommand*{\Leadsto}{\ensuremath{\leadsto}}</code> in the 0701 preamble and then use <code>\Leadsto</code> instead. 0702 </p> 0703 </dd> 0704 <dt><code>\Leftarrow</code> 0705 <a name="index-_005cLeftarrow"></a> 0706 </dt> 0707 <dd><p>⇐ Is implied by, double-line left arrow (relation). Similar: 0708 single-line left arrow <code>\leftarrow</code>. 0709 </p> 0710 </dd> 0711 <dt><code>\leftarrow</code> 0712 <a name="index-_005cleftarrow"></a> 0713 </dt> 0714 <dd><p>← Single-line left arrow (relation). 0715 Synonym: <code>\gets</code>. Similar: double-line left 0716 arrow <code>\Leftarrow</code>. 0717 </p> 0718 </dd> 0719 <dt><code>\leftharpoondown</code> 0720 <a name="index-_005cleftharpoondown"></a> 0721 </dt> 0722 <dd><p>↽ Single-line left harpoon, barb under bar (relation). 0723 </p> 0724 </dd> 0725 <dt><code>\leftharpoonup</code> 0726 <a name="index-_005cleftharpoonup"></a> 0727 </dt> 0728 <dd><p>↼ Single-line left harpoon, barb over bar (relation). 0729 </p> 0730 </dd> 0731 <dt><code>\Leftrightarrow</code> 0732 <a name="index-_005cLeftrightarrow"></a> 0733 </dt> 0734 <dd><p>⇔ Bi-implication; double-line double-headed arrow (relation). 0735 Similar: single-line double headed arrow <code>\leftrightarrow</code>. 0736 </p> 0737 </dd> 0738 <dt><code>\leftrightarrow</code> 0739 <a name="index-_005cleftrightarrow"></a> 0740 </dt> 0741 <dd><p>↔ Single-line double-headed arrow (relation). Similar: 0742 double-line double headed arrow <code>\Leftrightarrow</code>. 0743 </p> 0744 </dd> 0745 <dt><code>\leq</code> 0746 <a name="index-_005cleq"></a> 0747 </dt> 0748 <dd><p>≤ Less than or equal to (relation). This is a synonym 0749 for <code>\le</code>. 0750 </p> 0751 </dd> 0752 <dt><code>\lfloor</code> 0753 <a name="index-_005clfloor"></a> 0754 </dt> 0755 <dd><p>⌊ Left floor bracket (opening). Matches: <code>\floor</code>. 0756 </p> 0757 </dd> 0758 <dt><code>\lhd</code> 0759 <a name="index-_005clhd"></a> 0760 </dt> 0761 <dd><p>◁ Arrowhead, that is, triangle, pointing left (binary). 0762 For the normal subgroup symbol you should load 0763 <samp>amssymb</samp> and use <code>\vartriangleleft</code> (which is a relation 0764 and so gives better spacing). 0765 </p> 0766 </dd> 0767 <dt><code>\ll</code> 0768 <a name="index-_005cll"></a> 0769 </dt> 0770 <dd><p>≪ Much less than (relation). Similar: much greater 0771 than <code>\gg</code>. 0772 </p> 0773 </dd> 0774 <dt><code>\lnot</code> 0775 <a name="index-_005clnot"></a> 0776 </dt> 0777 <dd><p>¬ Logical negation (ordinary). Synonym: <code>\neg</code>. 0778 </p> 0779 </dd> 0780 <dt><code>\longleftarrow</code> 0781 <a name="index-_005clongleftarrow"></a> 0782 </dt> 0783 <dd><p>⟵ Long single-line left arrow (relation). Similar: long 0784 double-line left arrow <code>\Longleftarrow</code>. 0785 </p> 0786 </dd> 0787 <dt><code>\longleftrightarrow</code> 0788 <a name="index-_005clongleftrightarrow"></a> 0789 </dt> 0790 <dd><p>⟷ Long single-line double-headed arrow (relation). Similar: long 0791 double-line double-headed arrow <code>\Longleftrightarrow</code>. 0792 </p> 0793 </dd> 0794 <dt><code>\longmapsto</code> 0795 <a name="index-_005clongmapsto"></a> 0796 </dt> 0797 <dd><p>⟼ Long single-line left arrow starting with vertical bar 0798 (relation). Similar: shorter version <code>\mapsto</code>. 0799 </p> 0800 </dd> 0801 <dt><code>\longrightarrow</code> 0802 <a name="index-_005clongrightarrow"></a> 0803 </dt> 0804 <dd><p>⟶ Long single-line right arrow (relation). Similar: long 0805 double-line right arrow <code>\Longrightarrow</code>. 0806 </p> 0807 </dd> 0808 <dt><code>\lor</code> 0809 <a name="index-_005clor"></a> 0810 </dt> 0811 <dd><p>∨ Logical or (binary). Synonym: wedge <code>\wedge</code>. 0812 </p> 0813 </dd> 0814 <dt><code>\mapsto</code> 0815 <a name="index-_005cmapsto"></a> 0816 </dt> 0817 <dd><p>↦ Single-line left arrow starting with vertical bar 0818 (relation). 0819 Similar: longer version <code>\longmapsto</code>. 0820 </p> 0821 </dd> 0822 <dt><code>\mho</code> 0823 <a name="index-_005cmho"></a> 0824 </dt> 0825 <dd><p>℧ Conductance, half-circle rotated capital omega (ordinary). 0826 </p> 0827 </dd> 0828 <dt><code>\mid</code> 0829 <a name="index-_005cmid"></a> 0830 </dt> 0831 <dd><p>∣ Single-line vertical bar (relation). A typical use of 0832 <code>\mid</code> is for a set <code>\{\, x \mid x\geq 5 \,\}</code>. 0833 </p> 0834 <p>Similar: <code>\vert</code> and <code>|</code> produce the same single-line 0835 vertical bar symbol but without any spacing (they fall in class 0836 ordinary) and you should not use them as relations but instead only as 0837 ordinals, i.e., footnote symbols. For absolute value, see the entry 0838 for <code>\vert</code> and for norm see the entry for <code>\Vert</code>. 0839 </p> 0840 </dd> 0841 <dt><code>\models</code> 0842 <a name="index-_005cmodels"></a> 0843 </dt> 0844 <dd><p>⊨ Entails, or satisfies; double turnstile, short double dash 0845 (relation). Similar: long double dash <code>\vDash</code>. 0846 </p> 0847 </dd> 0848 <dt><code>\mp</code> 0849 <a name="index-_005cmp"></a> 0850 </dt> 0851 <dd><p>∓ Minus or plus (relation). 0852 </p> 0853 </dd> 0854 <dt><code>\mu</code> 0855 <a name="index-_005cmu"></a> 0856 </dt> 0857 <dd><p>μ Lowercase Greek letter (ordinary). 0858 </p> 0859 </dd> 0860 <dt><code>\nabla</code> 0861 <a name="index-_005cnabla"></a> 0862 </dt> 0863 <dd><p>∇ Hamilton’s del, or differential, operator (ordinary). 0864 </p> 0865 </dd> 0866 <dt><code>\natural</code> 0867 <a name="index-_005cnatural"></a> 0868 </dt> 0869 <dd><p>♮ Musical natural notation (ordinary). 0870 </p> 0871 </dd> 0872 <dt><code>\ne</code> 0873 <a name="index-_005cne"></a> 0874 </dt> 0875 <dd><p>≠ Not equal (relation). Synonym: <code>\neq</code>. 0876 </p> 0877 </dd> 0878 <dt><code>\nearrow</code> 0879 <a name="index-_005cnearrow"></a> 0880 </dt> 0881 <dd><p>↗ North-east arrow (relation). 0882 </p> 0883 </dd> 0884 <dt><code>\neg</code> 0885 <a name="index-_005cneg"></a> 0886 </dt> 0887 <dd><p>¬ Logical negation (ordinary). 0888 Synonym: <code>\lnot</code>. Sometimes instead used for 0889 negation: <code>\sim</code>. 0890 </p> 0891 </dd> 0892 <dt><code>\neq</code> 0893 <a name="index-_005cneq"></a> 0894 </dt> 0895 <dd><p>≠ Not equal (relation). Synonym: <code>\ne</code>. 0896 </p> 0897 </dd> 0898 <dt><code>\ni</code> 0899 <a name="index-_005cni"></a> 0900 </dt> 0901 <dd><p>∋ Reflected membership epsilon; has the member 0902 (relation). Synonym: <code>\owns</code>. Similar: is a member 0903 of <code>\in</code>. 0904 </p> 0905 </dd> 0906 <dt><code>\not</code> 0907 <a name="index-_005cnot"></a> 0908 </dt> 0909 <dd><p>  Long solidus, or slash, used to overstrike a 0910 following operator (relation). 0911 </p> 0912 <p>Many negated operators are available that don’t require <code>\not</code>, 0913 particularly with the <samp>amssymb</samp> package. For example, <code>\notin</code> 0914 is typographically preferable to <code>\not\in</code>. 0915 </p> 0916 </dd> 0917 <dt><code>\notin</code> 0918 <a name="index-_005cnotin"></a> 0919 </dt> 0920 <dd><p>∉ Not an element of (relation). Similar: not subset 0921 of <code>\nsubseteq</code>. 0922 </p> 0923 </dd> 0924 <dt><code>\nu</code> 0925 <a name="index-_005cnu"></a> 0926 </dt> 0927 <dd><p>ν Lowercase Greek letter (ordinary). 0928 </p> 0929 </dd> 0930 <dt><code>\nwarrow</code> 0931 <a name="index-_005cnwarrow"></a> 0932 </dt> 0933 <dd><p>↖ North-west arrow (relation). 0934 </p> 0935 </dd> 0936 <dt><code>\odot</code> 0937 <a name="index-_005codot"></a> 0938 </dt> 0939 <dd><p>⊙ Dot inside a circle (binary). Similar: variable-sized 0940 operator <code>\bigodot</code>. 0941 </p> 0942 </dd> 0943 <dt><code>\oint</code> 0944 <a name="index-_005coint"></a> 0945 </dt> 0946 <dd><p>∮ Contour integral, integral with circle in the middle 0947 (operator). 0948 </p> 0949 </dd> 0950 <dt><code>\Omega</code> 0951 <a name="index-_005cOmega"></a> 0952 </dt> 0953 <dd><p>Ω uppercase Greek letter (ordinary). 0954 </p> 0955 </dd> 0956 <dt><code>\omega</code> 0957 <a name="index-_005comega"></a> 0958 </dt> 0959 <dd><p>ω Lowercase Greek letter (ordinary). 0960 </p> 0961 </dd> 0962 <dt><code>\ominus</code> 0963 <a name="index-_005cominus"></a> 0964 </dt> 0965 <dd><p>⊖ Minus sign, or dash, inside a circle (binary). 0966 </p> 0967 </dd> 0968 <dt><code>\oplus</code> 0969 <a name="index-_005coplus"></a> 0970 </dt> 0971 <dd><p>⊕ Plus sign inside a circle (binary). Similar: variable-sized 0972 operator <code>\bigoplus</code>. 0973 </p> 0974 </dd> 0975 <dt><code>\oslash</code> 0976 <a name="index-_005coslash"></a> 0977 </dt> 0978 <dd><p>⊘ Solidus, or slash, inside a circle (binary). 0979 </p> 0980 </dd> 0981 <dt><code>\otimes</code> 0982 <a name="index-_005cotimes"></a> 0983 </dt> 0984 <dd><p>⊗ Times sign, or cross, inside a circle (binary). Similar: 0985 variable-sized operator <code>\bigotimes</code>. 0986 </p> 0987 </dd> 0988 <dt><code>\owns</code> 0989 <a name="index-_005cowns"></a> 0990 </dt> 0991 <dd><p>∋ Reflected membership epsilon; has the member 0992 (relation). Synonym: <code>\ni</code>. Similar: is a member 0993 of <code>\in</code>. 0994 </p> 0995 </dd> 0996 <dt><code>\parallel</code> 0997 <a name="index-_005cparallel"></a> 0998 </dt> 0999 <dd><p>∥ Parallel (relation). Synonym: <code>\|</code>. 1000 </p> 1001 </dd> 1002 <dt><code>\partial</code> 1003 <a name="index-_005cpartial"></a> 1004 </dt> 1005 <dd><p>∂ Partial differential (ordinary). 1006 </p> 1007 </dd> 1008 <dt><code>\perp</code> 1009 <a name="index-_005cperp"></a> 1010 </dt> 1011 <dd><p>⟂ Perpendicular (relation). Similar: <code>\bot</code> uses the 1012 same glyph but the spacing is different because it is in the class 1013 ordinary. 1014 </p> 1015 </dd> 1016 <dt><code>\Phi</code> 1017 <a name="index-_005cPhi"></a> 1018 </dt> 1019 <dd><p>Φ Uppercase Greek letter (ordinary). 1020 </p> 1021 </dd> 1022 <dt><code>\phi</code> 1023 <a name="index-_005cphi"></a> 1024 </dt> 1025 <dd><p>ϕ Lowercase Greek letter (ordinary). The variant form is 1026 <code>\varphi</code> φ. 1027 </p> 1028 </dd> 1029 <dt><code>\Pi</code> 1030 <a name="index-_005cPi"></a> 1031 </dt> 1032 <dd><p>Π uppercase Greek letter (ordinary). 1033 </p> 1034 </dd> 1035 <dt><code>\pi</code> 1036 <a name="index-_005cpi"></a> 1037 </dt> 1038 <dd><p>π Lowercase Greek letter (ordinary). The variant form is 1039 <code>\varpi</code> ϖ. 1040 </p> 1041 </dd> 1042 <dt><code>\pm</code> 1043 <a name="index-_005cpm"></a> 1044 </dt> 1045 <dd><p>± Plus or minus (binary). 1046 </p> 1047 </dd> 1048 <dt><code>\prec</code> 1049 <a name="index-_005cprec"></a> 1050 </dt> 1051 <dd><p>≺ Precedes (relation). Similar: less than <code><</code>. 1052 </p> 1053 </dd> 1054 <dt><code>\preceq</code> 1055 <a name="index-_005cpreceq"></a> 1056 </dt> 1057 <dd><p>⪯ Precedes or equals (relation). Similar: less than or 1058 equals <code>\leq</code>. 1059 </p> 1060 </dd> 1061 <dt><code>\prime</code> 1062 <a name="index-_005cprime"></a> 1063 </dt> 1064 <dd><p>′ Prime, or minute in a time expression (ordinary). 1065 Typically used as a superscript: <code>$f^\prime$</code>; <code>$f^\prime$</code> 1066 and <code>$f'$</code> produce the same result. An advantage of the second 1067 is that <code>$f'''$</code> produces the desired symbol, that is, the same 1068 result as <code>$f^{\prime\prime\prime}$</code>, but uses rather less 1069 typing. You can only use <code>\prime</code> in math mode. Using the right 1070 single quote <code>'</code> in text mode produces a different character 1071 (apostrophe). 1072 </p> 1073 </dd> 1074 <dt><code>\prod</code> 1075 <a name="index-_005cprod"></a> 1076 </dt> 1077 <dd><p>∏ Product (operator). 1078 </p> 1079 </dd> 1080 <dt><code>\propto</code> 1081 <a name="index-_005cpropto"></a> 1082 </dt> 1083 <dd><p>∝ Is proportional to (relation) 1084 </p> 1085 </dd> 1086 <dt><code>\Psi</code> 1087 <a name="index-_005cPsi"></a> 1088 </dt> 1089 <dd><p>Ψ uppercase Greek letter (ordinary). 1090 </p> 1091 </dd> 1092 <dt><code>\psi</code> 1093 <a name="index-_005cpsi"></a> 1094 </dt> 1095 <dd><p>ψ Lowercase Greek letter (ordinary). 1096 </p> 1097 </dd> 1098 <dt><code>\rangle</code> 1099 <a name="index-_005crangle"></a> 1100 </dt> 1101 <dd><p>⟩ Right angle, or sequence, bracket (closing). 1102 Similar: greater than <code>></code>. Matches:<code>\langle</code>. 1103 </p> 1104 </dd> 1105 <dt><code>\rbrace</code> 1106 <a name="index-_005crbrace"></a> 1107 </dt> 1108 <dd><p>} Right curly brace 1109 (closing). Synonym: <code>\}</code>. Matches <code>\lbrace</code>. 1110 </p> 1111 </dd> 1112 <dt><code>\rbrack</code> 1113 <a name="index-_005crbrack"></a> 1114 </dt> 1115 <dd><p>] Right square bracket 1116 (closing). Synonym: <code>]</code>. Matches <code>\lbrack</code>. 1117 </p> 1118 </dd> 1119 <dt><code>\rceil</code> 1120 <a name="index-_005crceil"></a> 1121 </dt> 1122 <dd><p>⌉ Right ceiling bracket (closing). Matches <code>\lceil</code>. 1123 </p> 1124 </dd> 1125 <dt><code>\Re</code> 1126 <a name="index-_005cRe"></a> 1127 </dt> 1128 <dd><p>ℜ Real part, real numbers, cursive capital R (ordinary). Related: 1129 double-line, or blackboard bold, R <code>\mathbb{R}</code>; to access 1130 this, load the <samp>amsfonts</samp> package. 1131 </p> 1132 </dd> 1133 <dt><code>\restriction</code> 1134 <a name="index-_005crestriction"></a> 1135 </dt> 1136 <dd><p>↾ Restriction of a function (relation). Synonym: 1137 <code>\upharpoonright</code>. Not available in plain TeX. In LaTeX you need to load the <samp>amssymb</samp> package. 1138 </p> 1139 </dd> 1140 <dt><code>\revemptyset</code> 1141 <a name="index-_005crevemptyset"></a> 1142 </dt> 1143 <dd><p>⦰ Reversed empty set symbol (ordinary). Related: 1144 <code>\varnothing</code>. Not available in plain TeX. In LaTeX you need to load the <samp>stix</samp> package. 1145 </p> 1146 </dd> 1147 <dt><code>\rfloor</code> 1148 <a name="index-_005crfloor"></a> 1149 </dt> 1150 <dd><p>⌋ Right floor bracket, a right square bracket with the top cut 1151 off (closing). Matches <code>\lfloor</code>. 1152 </p> 1153 </dd> 1154 <dt><code>\rhd</code> 1155 <a name="index-_005crhd"></a> 1156 </dt> 1157 <dd><p>◁ Arrowhead, that is, triangle, pointing right (binary). 1158 For the normal subgroup symbol you should instead 1159 load <samp>amssymb</samp> and use <code>\vartriangleright</code> (which is a 1160 relation and so gives better spacing). 1161 </p> 1162 </dd> 1163 <dt><code>\rho</code> 1164 <a name="index-_005crho"></a> 1165 </dt> 1166 <dd><p>ρ Lowercase Greek letter (ordinary). The variant form is 1167 <code>\varrho</code> ϱ. 1168 </p> 1169 </dd> 1170 <dt><code>\Rightarrow</code> 1171 <a name="index-_005cRightarrow"></a> 1172 </dt> 1173 <dd><p>⇒ Implies, right-pointing double line arrow 1174 (relation). Similar: right single-line arrow <code>\rightarrow</code>. 1175 </p> 1176 </dd> 1177 <dt><code>\rightarrow</code> 1178 <a name="index-_005crightarrow"></a> 1179 </dt> 1180 <dd><p>→ Right-pointing single line arrow (relation). 1181 Synonym: <code>\to</code>. Similar: right double line 1182 arrow <code>\Rightarrow</code>. 1183 </p> 1184 </dd> 1185 <dt><code>\rightharpoondown</code> 1186 <a name="index-_005crightharpoondown"></a> 1187 </dt> 1188 <dd><p>⇁ Right-pointing harpoon with barb below 1189 the line (relation). 1190 </p> 1191 </dd> 1192 <dt><code>\rightharpoonup</code> 1193 <a name="index-_005crightharpoonup"></a> 1194 </dt> 1195 <dd><p>⇀ Right-pointing harpoon with barb above the 1196 line (relation). 1197 </p> 1198 </dd> 1199 <dt><code>\rightleftharpoons</code> 1200 <a name="index-_005crightleftharpoons"></a> 1201 </dt> 1202 <dd><p>⇌ Right harpoon up above left harpoon down 1203 (relation). 1204 </p> 1205 </dd> 1206 <dt><code>\searrow</code> 1207 <a name="index-_005csearrow"></a> 1208 </dt> 1209 <dd><p>↘ Arrow pointing southeast (relation). 1210 </p> 1211 </dd> 1212 <dt><code>\setminus</code> 1213 <a name="index-_005csetminus"></a> 1214 </dt> 1215 <dd><p>⧵ Set difference, reverse solidus or reverse slash, 1216 like \ (binary). Similar: backslash <code>\backslash</code> and also 1217 <code>\textbackslash</code> outside of math mode. 1218 </p> 1219 </dd> 1220 <dt><code>\sharp</code> 1221 <a name="index-_005csharp"></a> 1222 </dt> 1223 <dd><p>♯ Musical sharp (ordinary). 1224 </p> 1225 </dd> 1226 <dt><code>\Sigma</code> 1227 <a name="index-_005cSigma"></a> 1228 </dt> 1229 <dd><p>Σ uppercase Greek letter (ordinary). 1230 </p> 1231 </dd> 1232 <dt><code>\sigma</code> 1233 <a name="index-_005csigma"></a> 1234 </dt> 1235 <dd><p>σ Lowercase Greek letter (ordinary). The variant form is 1236 <code>\varsigma</code> ς. 1237 </p> 1238 </dd> 1239 <dt><code>\sim</code> 1240 <a name="index-_005csim"></a> 1241 </dt> 1242 <dd><p>∼ Similar, in a relation (relation). 1243 </p> 1244 </dd> 1245 <dt><code>\simeq</code> 1246 <a name="index-_005csimeq"></a> 1247 </dt> 1248 <dd><p>≃ Similar or equal to, in a relation (relation). 1249 </p> 1250 </dd> 1251 <dt><code>\smallint</code> 1252 <a name="index-_005csmallint"></a> 1253 </dt> 1254 <dd><p>∫ Integral sign that does not change to a larger size in a 1255 display (operator). 1256 </p> 1257 </dd> 1258 <dt><code>\smile</code> 1259 <a name="index-_005csmile"></a> 1260 </dt> 1261 <dd><p>⌣ Upward curving arc, smile (ordinary). 1262 </p> 1263 </dd> 1264 <dt><code>\spadesuit</code> 1265 <a name="index-_005cspadesuit"></a> 1266 </dt> 1267 <dd><p>♠ Spade card suit (ordinary). 1268 </p> 1269 </dd> 1270 <dt><code>\sqcap</code> 1271 <a name="index-_005csqcap"></a> 1272 </dt> 1273 <dd><p>⊓ Square intersection symbol (binary). Similar: 1274 intersection <code>cap</code>. 1275 </p> 1276 </dd> 1277 <dt><code>\sqcup</code> 1278 <a name="index-_005csqcup"></a> 1279 </dt> 1280 <dd><p>⊔ Square union symbol (binary). Similar: 1281 union <code>cup</code>. Related: variable-sized 1282 operator <code>\bigsqcup</code>. 1283 </p> 1284 </dd> 1285 <dt><code>\sqsubset</code> 1286 <a name="index-_005csqsubset"></a> 1287 </dt> 1288 <dd><p>⊏ Square subset symbol (relation). Similar: 1289 subset <code>\subset</code>. Not available in plain TeX. In LaTeX you need to load the <samp>amssymb</samp> package. 1290 </p> 1291 </dd> 1292 <dt><code>\sqsubseteq</code> 1293 <a name="index-_005csqsubseteq"></a> 1294 </dt> 1295 <dd><p>⊑ Square subset or equal symbol (binary). Similar: subset or 1296 equal to <code>\subseteq</code>. 1297 </p> 1298 </dd> 1299 <dt><code>\sqsupset</code> 1300 <a name="index-_005csqsupset"></a> 1301 </dt> 1302 <dd><p>⊐ Square superset symbol (relation). Similar: 1303 superset <code>\supset</code>. Not available in plain TeX. In LaTeX you need to load the <samp>amssymb</samp> package. 1304 </p> 1305 </dd> 1306 <dt><code>\sqsupseteq</code> 1307 <a name="index-_005csqsupseteq"></a> 1308 </dt> 1309 <dd><p>⊒ Square superset or equal symbol (binary). 1310 Similar: superset or equal <code>\supseteq</code>. 1311 </p> 1312 </dd> 1313 <dt><code>\star</code> 1314 <a name="index-_005cstar"></a> 1315 </dt> 1316 <dd><p>⋆ Five-pointed star, sometimes used as a general binary 1317 operation but sometimes reserved for cross-correlation (binary). 1318 Similar: the synonyms asterisk <code>*</code> and <code>\ast</code>, which 1319 are six-pointed, and more often appear as a superscript or subscript, 1320 as with the Kleene star. 1321 </p> 1322 </dd> 1323 <dt><code>\subset</code> 1324 <a name="index-_005csubset"></a> 1325 </dt> 1326 <dd><p>⊂ Subset (occasionally, is implied by) (relation). 1327 </p> 1328 </dd> 1329 <dt><code>\subseteq</code> 1330 <a name="index-_005csubseteq"></a> 1331 </dt> 1332 <dd><p>⊆ Subset or equal to (relation). 1333 </p> 1334 </dd> 1335 <dt><code>\succ</code> 1336 <a name="index-_005csucc"></a> 1337 </dt> 1338 <dd><p>≻ Comes after, succeeds (relation). Similar: is less 1339 than <code>></code>. 1340 </p> 1341 </dd> 1342 <dt><code>\succeq</code> 1343 <a name="index-_005csucceq"></a> 1344 </dt> 1345 <dd><p>⪰ Succeeds or is equal to (relation). Similar: less 1346 than or equal to <code>\leq</code>. 1347 </p> 1348 </dd> 1349 <dt><code>\sum</code> 1350 <a name="index-_005csum"></a> 1351 </dt> 1352 <dd><p>∑ Summation (operator). Similar: Greek capital 1353 sigma <code>\Sigma</code>. 1354 </p> 1355 </dd> 1356 <dt><code>\supset</code> 1357 <a name="index-_005csupset"></a> 1358 </dt> 1359 <dd><p>⊃ Superset (relation). 1360 </p> 1361 </dd> 1362 <dt><code>\supseteq</code> 1363 <a name="index-_005csupseteq"></a> 1364 </dt> 1365 <dd><p>⊇ Superset or equal to (relation). 1366 </p> 1367 </dd> 1368 <dt><code>\surd</code> 1369 <a name="index-_005csurd"></a> 1370 </dt> 1371 <dd><p>√ Radical symbol (ordinary). The LaTeX command 1372 <code>\sqrt{...}</code> typesets the square root of the argument, with a bar 1373 that extends to cover the argument. 1374 </p> 1375 </dd> 1376 <dt><code>\swarrow</code> 1377 <a name="index-_005cswarrow"></a> 1378 </dt> 1379 <dd><p>↙ Southwest-pointing arrow (relation). 1380 </p> 1381 </dd> 1382 <dt><code>\tau</code> 1383 <a name="index-_005ctau"></a> 1384 </dt> 1385 <dd><p>τ Lowercase Greek letter (ordinary). 1386 </p> 1387 </dd> 1388 <dt><code>\theta</code> 1389 <a name="index-_005ctheta"></a> 1390 </dt> 1391 <dd><p>θ Lowercase Greek letter (ordinary). The variant form is 1392 <code>\vartheta</code> ϑ. 1393 </p> 1394 </dd> 1395 <dt><code>\times</code> 1396 <a name="index-_005ctimes"></a> 1397 </dt> 1398 <dd><p>× Primary school multiplication sign (binary). See 1399 also <code>\cdot</code>. 1400 </p> 1401 </dd> 1402 <dt><code>\to</code> 1403 <a name="index-_005cto"></a> 1404 </dt> 1405 <dd><p>→ Right-pointing single line arrow (relation). 1406 Synonym: <code>\rightarrow</code>. 1407 </p> 1408 </dd> 1409 <dt><code>\top</code> 1410 <a name="index-_005ctop"></a> 1411 </dt> 1412 <dd><p>⊤ Top, greatest element of a partially ordered set 1413 (ordinary). See also <code>\bot</code>. 1414 </p> 1415 </dd> 1416 <dt><code>\triangle</code> 1417 <a name="index-_005ctriangle"></a> 1418 </dt> 1419 <dd><p>△ Triangle (ordinary). 1420 </p> 1421 </dd> 1422 <dt><code>\triangleleft</code> 1423 <a name="index-_005ctriangleleft"></a> 1424 </dt> 1425 <dd><p>◁ Not-filled triangle pointing left 1426 (binary). Similar: <code>\lhd</code>. For the normal subgroup symbol you 1427 should load <samp>amssymb</samp> and use <code>\vartriangleleft</code> (which 1428 is a relation and so gives better spacing). 1429 </p> 1430 </dd> 1431 <dt><code>\triangleright</code> 1432 <a name="index-_005ctriangleright"></a> 1433 </dt> 1434 <dd><p>▷ Not-filled triangle pointing right 1435 (binary). For the normal subgroup symbol you should instead load 1436 <samp>amssymb</samp> and use <code>\vartriangleright</code> (which is a 1437 relation and so gives better spacing). 1438 </p> 1439 </dd> 1440 <dt><code>\unlhd</code> 1441 <a name="index-_005cunlhd"></a> 1442 </dt> 1443 <dd><p>⊴ Left-pointing not-filled underlined arrowhead, that is, 1444 triangle, with a line under (binary). For the 1445 normal subgroup symbol load <samp>amssymb</samp> and 1446 use <code>\vartrianglelefteq</code> (which is a relation and so gives 1447 better spacing). 1448 </p> 1449 </dd> 1450 <dt><code>\unrhd</code> 1451 <a name="index-_005cunrhd"></a> 1452 </dt> 1453 <dd><p>⊵ Right-pointing not-filled underlined arrowhead, that is, 1454 triangle, with a line under (binary). For the 1455 normal subgroup symbol load <samp>amssymb</samp> and 1456 use <code>\vartrianglerighteq</code> (which is a relation and so gives 1457 better spacing). 1458 </p> 1459 </dd> 1460 <dt><code>\Uparrow</code> 1461 <a name="index-_005cUparrow"></a> 1462 </dt> 1463 <dd><p>⇑ Double-line upward-pointing arrow 1464 (relation). Similar: single-line up-pointing 1465 arrow <code>\uparrow</code>. 1466 </p> 1467 </dd> 1468 <dt><code>\uparrow</code> 1469 <a name="index-_005cuparrow"></a> 1470 </dt> 1471 <dd><p>↑ Single-line upward-pointing arrow, diverges 1472 (relation). Similar: double-line up-pointing 1473 arrow <code>\Uparrow</code>. 1474 </p> 1475 </dd> 1476 <dt><code>\Updownarrow</code> 1477 <a name="index-_005cUpdownarrow"></a> 1478 </dt> 1479 <dd><p>⇕ Double-line upward-and-downward-pointing arrow 1480 (relation). Similar: single-line upward-and-downward-pointing 1481 arrow <code>\updownarrow</code>. 1482 </p> 1483 </dd> 1484 <dt><code>\updownarrow</code> 1485 <a name="index-_005cupdownarrow"></a> 1486 </dt> 1487 <dd><p>↕ Single-line upward-and-downward-pointing arrow 1488 (relation). Similar: double-line upward-and-downward-pointing 1489 arrow <code>\Updownarrow</code>. 1490 </p> 1491 </dd> 1492 <dt><code>\upharpoonright</code> 1493 <a name="index-_005cupharpoonright"></a> 1494 </dt> 1495 <dd><p>↾ Up harpoon, with barb on right side 1496 (relation). Synonym: <code>\restriction</code>. 1497 Not available in plain TeX. In LaTeX you need to load the <samp>amssymb</samp> package. 1498 </p> 1499 </dd> 1500 <dt><code>\uplus</code> 1501 <a name="index-_005cuplus"></a> 1502 </dt> 1503 <dd><p>⊎ Multiset union, a union symbol with a plus symbol in 1504 the middle (binary). Similar: union <code>\cup</code>. Related: 1505 variable-sized operator <code>\biguplus</code>. 1506 </p> 1507 </dd> 1508 <dt><code>\Upsilon</code> 1509 <a name="index-_005cUpsilon"></a> 1510 </dt> 1511 <dd><p>Υ uppercase Greek letter (ordinary). 1512 </p> 1513 </dd> 1514 <dt><code>\upsilon</code> 1515 <a name="index-_005cupsilon"></a> 1516 </dt> 1517 <dd><p>υ Lowercase Greek letter (ordinary). 1518 </p> 1519 </dd> 1520 <dt><code>\varepsilon</code> 1521 <a name="index-_005cvarepsilon"></a> 1522 </dt> 1523 <dd><p>ε Small letter script epsilon (ordinary). This is 1524 more widely used in mathematics than the non-variant lunate epsilon form 1525 <code>\epsilon</code> ϵ. Related: set 1526 membership <code>\in</code>. 1527 </p> 1528 </dd> 1529 <dt><code>\vanothing</code> 1530 <a name="index-_005cvanothing"></a> 1531 </dt> 1532 <dd><p>∅ Empty set symbol. Similar: <code>\emptyset</code>. Related: 1533 <code>\revemptyset</code>. Not available in plain TeX. In LaTeX you need to load the <samp>amssymb</samp> package. 1534 </p> 1535 </dd> 1536 <dt><code>\varphi</code> 1537 <a name="index-_005cvarphi"></a> 1538 </dt> 1539 <dd><p>φ Variant on the lowercase Greek letter (ordinary). 1540 The non-variant form is <code>\phi</code> ϕ. 1541 </p> 1542 </dd> 1543 <dt><code>\varpi</code> 1544 <a name="index-_005cvarpi"></a> 1545 </dt> 1546 <dd><p>ϖ Variant on the lowercase Greek letter (ordinary). 1547 The non-variant form is <code>\pi</code> π. 1548 </p> 1549 </dd> 1550 <dt><code>\varrho</code> 1551 <a name="index-_005cvarrho"></a> 1552 </dt> 1553 <dd><p>ϱ Variant on the lowercase Greek letter (ordinary). 1554 The non-variant form is <code>\rho</code> ρ. 1555 </p> 1556 </dd> 1557 <dt><code>\varsigma</code> 1558 <a name="index-_005cvarsigma"></a> 1559 </dt> 1560 <dd><p>ς Variant on the lowercase Greek letter 1561 (ordinary). The non-variant form is 1562 <code>\sigma</code> σ. 1563 </p> 1564 </dd> 1565 <dt><code>\vartheta</code> 1566 <a name="index-_005cvartheta"></a> 1567 </dt> 1568 <dd><p>ϑ Variant on the lowercase Greek letter 1569 (ordinary). The non-variant form is 1570 <code>\theta</code> θ. 1571 </p> 1572 </dd> 1573 <dt><code>\vdash</code> 1574 <a name="index-_005cvdash"></a> 1575 </dt> 1576 <dd><p>⊢ Provable; turnstile, vertical and a dash 1577 (relation). Similar: turnstile rotated a 1578 half-circle <code>\dashv</code>. 1579 </p> 1580 </dd> 1581 <dt><code>\vee</code> 1582 <a name="index-_005cvee"></a> 1583 </dt> 1584 <dd><p>∨ Logical or; a downwards v shape (binary). Related: 1585 logical and <code>\wedge</code>. Similar: variable-sized 1586 operator <code>\bigvee</code>. 1587 </p> 1588 </dd> 1589 <dt><code>\Vert</code> 1590 <a name="index-_005cVert"></a> 1591 </dt> 1592 <dd><p>‖ Vertical double bar (ordinary). Similar: vertical single 1593 bar <code>\vert</code>. 1594 </p> 1595 <p>For a norm symbol, you can use the <samp>mathtools</samp> package and put in 1596 your preamble 1597 <code>\DeclarePairedDelimiter\norm{\lVert}{\rVert}</code>. This creates 1598 three command variants for double-line vertical bars that are correctly 1599 horizontally spaced: if in the document body you write the starred 1600 version <code>$\norm*{M^\perp}$</code> then the height of the vertical bars 1601 will match the height of the argument, whereas with 1602 <code>\norm{M^\perp}</code> the bars do not grow with the height of the 1603 argument but instead are the default height, and <code>\norm[<var>size 1604 command</var>]{M^\perp}</code> also gives bars that do not grow but are set to 1605 the size given in the <var>size command</var>, e.g., <code>\Bigg</code>. 1606 </p> 1607 </dd> 1608 <dt><code>\vert</code> 1609 <a name="index-_005cvert"></a> 1610 </dt> 1611 <dd><p>| Single line vertical bar (ordinary). Similar: double-line 1612 vertical bar <code>\Vert</code>. For such that, as in the definition of a 1613 set, use <code>\mid</code> because it is a relation. 1614 </p> 1615 <p>For absolute value you can use the <samp>mathtools</samp> package and in your 1616 preamble put 1617 <code>\DeclarePairedDelimiter\abs{\lvert}{\rvert}</code>. This creates 1618 three command variants for single-line vertical bars that are correctly 1619 horizontally spaced: if in the document body you write the starred 1620 version <code>$\abs*{\frac{22}{7}}$</code> then the height of the 1621 vertical bars will match the height of the argument, whereas with 1622 <code>\abs{\frac{22}{7}}</code> the bars do not grow with the height of 1623 the argument but instead are the default height, and 1624 <code>\abs[<var>size command</var>]{\frac{22}{7}}</code> also gives bars that 1625 do not grow but are set to the size given in the <var>size command</var>, 1626 e.g., <code>\Bigg</code>. 1627 </p> 1628 </dd> 1629 <dt><code>\wedge</code> 1630 <a name="index-_005cwedge"></a> 1631 </dt> 1632 <dd><p>∧ Logical and (binary). Synonym: <code>\land</code>. See also 1633 logical or <code>\vee</code>. Similar: variable-sized 1634 operator <code>\bigwedge</code>. 1635 </p> 1636 </dd> 1637 <dt><code>\wp</code> 1638 <a name="index-_005cwp"></a> 1639 </dt> 1640 <dd><p>℘ Weierstrass p (ordinary). 1641 </p> 1642 </dd> 1643 <dt><code>\wr</code> 1644 <a name="index-_005cwr"></a> 1645 </dt> 1646 <dd><p>≀ Wreath product (binary). 1647 </p> 1648 </dd> 1649 <dt><code>\Xi</code> 1650 <a name="index-_005cXi"></a> 1651 </dt> 1652 <dd><p>Ξ uppercase Greek letter (ordinary). 1653 </p> 1654 </dd> 1655 <dt><code>\xi</code> 1656 <a name="index-_005cxi"></a> 1657 </dt> 1658 <dd><p>ξ Lowercase Greek letter (ordinary). 1659 </p> 1660 </dd> 1661 <dt><code>\zeta</code> 1662 <a name="index-_005czeta"></a> 1663 </dt> 1664 <dd><p>ζ Lowercase Greek letter (ordinary). 1665 </p> 1666 </dd> 1667 </dl> 1668 1669 <p>The following symbols are most often used in plain text but LaTeX 1670 provides versions to use in mathematical text. 1671 </p> 1672 <dl compact="compact"> 1673 <dt><code>\mathdollar</code> 1674 <a name="index-_005cmathdollar"></a> 1675 </dt> 1676 <dd><p>Dollar sign in math mode: $. 1677 </p> 1678 </dd> 1679 <dt><code>\mathparagraph</code> 1680 <a name="index-_005cmathparagraph"></a> 1681 </dt> 1682 <dd><p>Paragraph sign (pilcrow) in math mode, ¶. 1683 </p> 1684 </dd> 1685 <dt><code>\mathsection</code> 1686 <a name="index-_005cmathsection"></a> 1687 </dt> 1688 <dd><p>Section sign in math mode §. 1689 </p> 1690 </dd> 1691 <dt><code>\mathsterling</code> 1692 <a name="index-_005cmathsterling"></a> 1693 </dt> 1694 <dd><p>Sterling sign in math mode: £. 1695 </p> 1696 </dd> 1697 <dt><code>\mathunderscore</code> 1698 <a name="index-_005cmathunderscore"></a> 1699 </dt> 1700 <dd><p>Underscore in math mode: _. 1701 </p> 1702 </dd> 1703 </dl> 1704 1705 <table class="menu" border="0" cellspacing="0"> 1706 <tr><td align="left" valign="top">• <a href="Arrows.html#Arrows" accesskey="1">Arrows</a>:</td><td> </td><td align="left" valign="top">List of arrows. 1707 </td></tr> 1708 <tr><td align="left" valign="top">• <a href="_005cboldmath-_0026-_005cunboldmath.html#g_t_005cboldmath-_0026-_005cunboldmath" accesskey="2">\boldmath & \unboldmath</a>:</td><td> </td><td align="left" valign="top">Symbols in boldface. 1709 </td></tr> 1710 <tr><td align="left" valign="top">• <a href="Blackboard-bold.html#Blackboard-bold" accesskey="3">Blackboard bold</a>:</td><td> </td><td align="left" valign="top">Doublestruck characters. 1711 </td></tr> 1712 <tr><td align="left" valign="top">• <a href="Calligraphic.html#Calligraphic" accesskey="4">Calligraphic</a>:</td><td> </td><td align="left" valign="top">Cursive characters. 1713 </td></tr> 1714 <tr><td align="left" valign="top">• <a href="Delimiters.html#Delimiters" accesskey="5">Delimiters</a>:</td><td> </td><td align="left" valign="top">Parentheses, braces, etc. 1715 </td></tr> 1716 <tr><td align="left" valign="top">• <a href="Dots.html#Dots" accesskey="6">Dots</a>:</td><td> </td><td align="left" valign="top">Ellipses, etc. 1717 </td></tr> 1718 <tr><td align="left" valign="top">• <a href="Greek-letters.html#Greek-letters" accesskey="7">Greek letters</a>:</td><td> </td><td align="left" valign="top">List of Greek letters. 1719 </td></tr> 1720 </table> 1721 1722 1723 1724 1725 <hr/><div class='referenceinfo'> <a href='https://latexref.xyz/'> <i>Unofficial LaTeX2e reference manual</i></a></div> 1726 </body> 1727 </html>