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Table of mathematical symbols by introduction date
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<p>The following table lists many specialized <a href="/facts/Symbols/GS8mTn0h">symbols</a> commonly used in modern <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title. </p> <table><tbody><tr><th>Symbol</th><th>Name</th><th>Date of earliest use</th><th>First author to use</th></tr><tr><td>—</td><td><a href="/facts/Obelus/016zu92X">horizontal bar for division</a></td><td>14th century (approx.)</td><td><a href="/facts/Nicole_Oresme/sv3C8R2s">Nicole Oresme</a></td></tr><tr><td>+</td><td><a href="/facts/Plus_and_minus_signs/6RJD4Xt9">plus sign</a></td><td>1360 (approx.), abbreviation for Latin <i>et</i> resembling the plus sign</td><td><a href="/facts/Nicole_Oresme/sv3C8R2s">Nicole Oresme</a></td></tr><tr><td>−</td><td><a href="/facts/Plus_and_minus_signs/6RJD4Xt9">minus sign</a></td><td>1489 (first appearance of minus sign, and also first appearance of plus sign in print)</td><td><a href="/facts/Johannes_Widmann/edAAMLtl">Johannes Widmann</a></td></tr><tr><td>√</td><td>radical symbol (for <a href="/facts/Square_root/AfrzfBdQ">square root</a>)</td><td>1525 (without the <a href="/facts/Vinculum_(symbol)/00m765V2">vinculum</a> above the <a href="/facts/Radicand/XrRjtJGe">radicand</a>)</td><td><a href="/facts/Christoff_Rudolff/awTVIfT8">Christoff Rudolff</a></td></tr><tr><td rowspan="2">(...)</td><td rowspan="2"><a href="/facts/Bracket/yzGM9J8A">parentheses</a> (for precedence grouping)</td><td>1544 (in handwritten notes)</td><td><a href="/facts/Michael_Stifel/PQMsGL9C">Michael Stifel</a></td></tr><tr><td>1556</td><td><a href="/facts/Niccol%C3%B2_Fontana_Tartaglia/BsB0Kupr">Niccolò Tartaglia</a></td></tr><tr><td>=</td><td><a href="/facts/Equals_sign/AweYSg9h">equals sign</a></td><td>1557</td><td><a href="/facts/Robert_Recorde/fLnLhLnY">Robert Recorde</a></td></tr><tr><td>.</td><td><a href="/facts/Decimal_separator/t6ocVouk">decimal separator</a></td><td>1593</td><td><a href="/facts/Christopher_Clavius/1mefR30R">Christopher Clavius</a></td></tr><tr><td>×</td><td><a href="/facts/Multiplication_sign/XtsHgIbs">multiplication sign</a></td><td>1618</td><td rowspan="3"><a href="/facts/William_Oughtred/2cyf4A1n">William Oughtred</a></td></tr><tr><td>±</td><td><a href="/facts/Plus%E2%80%93minus_sign/cAP8AgPH">plus–minus sign</a></td><td rowspan="2">1628</td></tr><tr><td>∷</td><td><a href="/facts/Proportion_sign/xDQmfh6t">proportion sign</a></td></tr><tr><td><i>n</i>√ </td><td>radical symbol (for <a href="/facts/Nth_root/XrRjtJGe"><i>n</i>th root</a>)</td><td>1629</td><td><a href="/facts/Albert_Girard/8GrSDTTC">Albert Girard</a></td></tr><tr><td><></td><td><a href="/facts/Strict_inequality/qkze4zdI">strict inequality</a> signs (<i>less-than sign</i> and <i>greater-than sign</i>)</td><td>1631</td><td><a href="/facts/Thomas_Harriot/rzo8f1Ll">Thomas Harriot</a></td></tr><tr><td rowspan="2"><i>xy</i> </td><td rowspan="2"><a href="/facts/Superscript/6tExBnkw">superscript</a> notation (for <a href="/facts/Exponentiation/pac6QY2g">exponentiation</a>)</td><td>1636 (using <a href="/facts/Roman_numerals/7BA8nn78">Roman numerals</a> as superscripts)</td><td><a href="/facts/James_Hume_(mathematician)/8f3ae5e6">James Hume</a></td></tr><tr><td>1637 (in the modern form)</td><td><a href="/facts/Ren%C3%A9_Descartes/ohqj6DMf">René Descartes</a> (<a href="/facts/La_G%C3%A9om%C3%A9trie/ELdb057s">La Géométrie</a>)</td></tr><tr><td><i>x</i> </td><td>Use of the letter <i>x</i> for an <a href="/facts/Independent_variable/dINfzIF2">independent variable</a> or unknown value. See <a href="/facts/History_of_algebra/duLGFrgf">History of algebra: The symbol <i>x</i></a>.</td><td>1637</td><td><a href="/facts/Ren%C3%A9_Descartes/ohqj6DMf">René Descartes</a> (<a href="/facts/La_G%C3%A9om%C3%A9trie/ELdb057s">La Géométrie</a>)</td></tr><tr><td>√ ̅ </td><td>radical symbol (for <a href="/facts/Square_root/AfrzfBdQ">square root</a>)</td><td>1637 (with the <a href="/facts/Vinculum_(symbol)/00m765V2">vinculum</a> above the <a href="/facts/Radicand/XrRjtJGe">radicand</a>)</td><td><a href="/facts/Ren%C3%A9_Descartes/ohqj6DMf">René Descartes</a> (<a href="/facts/La_G%C3%A9om%C3%A9trie/ELdb057s">La Géométrie</a>)</td></tr><tr><td>%</td><td><a href="/facts/Percent_sign/pLdHNKar">percent sign</a></td><td>1650 (approx.)</td><td>unknown</td></tr><tr><td>∞</td><td><a href="/facts/Infinity/cF506uD7">infinity</a> sign</td><td>1655</td><td><a href="/facts/John_Wallis/hlMcED3G">John Wallis</a></td></tr><tr><td>÷</td><td><a href="/facts/Division_sign/E83FFxSe">division sign</a> (a repurposed <a href="/facts/Obelus/016zu92X">obelus</a> variant)</td><td>1659</td><td><a href="/facts/Johann_Rahn/NxhDArK6">Johann Rahn</a></td></tr><tr><td rowspan="2">≤≥</td><td rowspan="2"><a href="/facts/Inequality_(mathematics)/qkze4zdI">unstrict inequality signs</a> (<i>less-than or equals to sign</i> and <i>greater-than or equals to sign</i>)</td><td>1670 (with the horizontal bar over the inequality sign, rather than below it)</td><td><a href="/facts/John_Wallis/hlMcED3G">John Wallis</a></td></tr><tr><td>1734 (with double horizontal bar below the inequality sign)</td><td><a href="/facts/Pierre_Bouguer/d7tuYCxr">Pierre Bouguer</a></td></tr><tr><td>d</td><td><a href="/facts/Differential_(calculus)/YmSDWCol">differential</a> sign</td><td rowspan="2">1675</td><td rowspan="4"><a href="/facts/Gottfried_Leibniz/cTc2er83">Gottfried Leibniz</a></td></tr><tr><td>∫</td><td><a href="/facts/Integral_sign/F7tlYEmF">integral sign</a></td></tr><tr><td>:</td><td><a href="/facts/Colon_(punctuation)/se9fjJa4">colon</a> (for <a href="/facts/Division_(mathematics)/FqLKNkmq">division</a>)</td><td>1684 (deriving from use of colon to denote fractions, dating back to 1633)</td></tr><tr><td>·</td><td><a href="/facts/Middle_dot/FqdEx1gT">middle dot</a> (for <a href="/facts/Multiplication/VtcUjpNv">multiplication</a>)</td><td>1698 (perhaps deriving from a much earlier use of middle dot to separate juxtaposed numbers)</td></tr><tr><td>⁄</td><td><a href="/facts/Slash_(punctuation)/fuaRyKzc">division slash</a> (a.k.a. <i>solidus</i>)</td><td>1718 (deriving from horizontal fraction bar, invented by <a href="/facts/Abu_Bakr_al-Hassar/5qyGNHKq">Abu Bakr al-Hassar</a> in the 12th century)</td><td><a href="/facts/Thomas_Twining_(merchant)/B4H26KdH">Thomas Twining</a></td></tr><tr><td>≠</td><td><a href="/facts/Inequality_(mathematics)/qkze4zdI">inequality</a> sign (<i>not equal to</i>)</td><td>unknown</td><td rowspan="3"><a href="/facts/Leonhard_Euler/z2fsbjgj">Leonhard Euler</a></td></tr><tr><td><i>x</i>′</td><td><a href="/facts/Prime_symbol/3p9EvU5X">prime symbol</a> (for <a href="/facts/Derivative/7Ito70Dh">derivative</a>)</td><td>1748</td></tr><tr><td>Σ</td><td><a href="/facts/Summation/V2WUxoKn">summation</a> symbol</td><td>1755</td></tr><tr><td>∝</td><td><a href="/facts/Proportionality_(mathematics)/xDQmfh6t">proportionality</a> sign</td><td>1768</td><td><a href="/facts/William_Emerson_(mathematician)/oXIAyK6P">William Emerson</a></td></tr><tr><td>∂</td><td><a href="/facts/Partial_differential/JWHsBkAu">partial differential</a> sign (a.k.a. <i>curly d</i> or <i><a href="/facts/Carl_Gustav_Jacob_Jacobi/4Syeauo5">Jacobi</a>'s delta</i>)</td><td>1770</td><td><a href="/facts/Marquis_de_Condorcet/DjXBUnIL">Marquis de Condorcet</a></td></tr><tr><td>≡</td><td><a href="/facts/Identity_(mathematics)/LR46j4uR">identity</a> sign (for <a href="/facts/Congruence_relation/TV3njpqF">congruence relation</a>)</td><td>1801 (first appearance in print; used previously in personal writings of Gauss)</td><td rowspan="2"><a href="/facts/Carl_Friedrich_Gauss/f4eSMBD7">Carl Friedrich Gauss</a></td></tr><tr><td>[<i>x</i>]</td><td><i>integral part</i> (a.k.a. <a href="/facts/Floor_and_ceiling_functions/ssehyMMf">floor</a>)</td><td>1808</td></tr><tr><td>!</td><td><a href="/facts/Factorial/kkfy1Bwe">factorial</a></td><td>1808</td><td><a href="/facts/Christian_Kramp/allRvwYD">Christian Kramp</a></td></tr><tr><td>Π</td><td><a href="/facts/Multiplication/VtcUjpNv">product</a> symbol</td><td>1812</td><td><a href="/facts/Carl_Friedrich_Gauss/f4eSMBD7">Carl Friedrich Gauss</a></td></tr><tr><td rowspan="2">⊂⊃</td><td rowspan="2"><a href="/facts/Set_inclusion/SJGERmbA">set inclusion</a> signs (<i>subset of</i>, <i>superset of</i>)</td><td>1817</td><td><a href="/facts/Joseph_Gergonne/B8ggHgVo">Joseph Gergonne</a></td></tr><tr><td>1890</td><td><a href="/facts/Ernst_Schr%C3%B6der_(mathematician)/GsUT8tID">Ernst Schröder</a></td></tr><tr><td rowspan="2">|...|</td><td><a href="/facts/Absolute_value/dwJBpEs5">absolute value</a> notation</td><td>1841</td><td><a href="/facts/Karl_Weierstrass/4U8vdQzL">Karl Weierstrass</a></td></tr><tr><td><a href="/facts/Determinant/eGYqJ2TF">determinant</a> of a matrix</td><td>1841</td><td rowspan="2"><a href="/facts/Arthur_Cayley/NBd7QkeE">Arthur Cayley</a></td></tr><tr><td>‖...‖</td><td><a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> notation</td><td>1843</td></tr><tr><td>∇</td><td><a href="/facts/Nabla_symbol/NtcnUmyW">nabla symbol</a> (for <a href="/facts/Vector_differential/0xEmQeBo">vector differential</a>)</td><td>1846 (previously used by Hamilton as a general-purpose operator sign)</td><td><a href="/facts/William_Rowan_Hamilton/U86CqUlt">William Rowan Hamilton</a></td></tr><tr><td>∩∪</td><td><a href="/facts/Intersection_(set_theory)/RPfUNJh9">intersection</a> <a href="/facts/Union_(set_theory)/KVVXKfWl">union</a></td><td>1888</td><td><a href="/facts/Giuseppe_Peano/VT2Wsmu7">Giuseppe Peano</a></td></tr><tr><td>ℵ</td><td><a href="/facts/Aleph_number/kwe9I4v5">aleph</a> symbol (for <a href="/facts/Transfinite_cardinal_number/m2oTjXaj">transfinite cardinal numbers</a>)</td><td>1893</td><td><a href="/facts/Georg_Cantor/k5v1DvW4">Georg Cantor</a></td></tr><tr><td>∈</td><td><a href="/facts/Membership_sign/SJGERmbA">membership sign</a> (<i>is <a href="/facts/Element_(mathematics)/Q2mx1vHL">an element</a> of</i>)</td><td>1894</td><td><a href="/facts/Giuseppe_Peano/VT2Wsmu7">Giuseppe Peano</a></td></tr><tr><td>O</td><td><a href="/facts/Big_O_Notation/weFFjSWg">Big O Notation</a></td><td>1894</td><td><a href="/facts/Paul_Bachmann/cc16kVy1">Paul Bachmann</a></td></tr><tr><td>{...}</td><td>braces, a.k.a. <a href="/facts/Curly_bracket/yzGM9J8A">curly brackets</a> (for <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> notation)</td><td>1895</td><td><a href="/facts/Georg_Cantor/k5v1DvW4">Georg Cantor</a></td></tr><tr><td> N {\displaystyle \mathbb {N} } </td><td><a href="/facts/Blackboard_bold/CGTmvA8H">Blackboard bold</a> capital N (for <a href="/facts/Natural_number/u65og8JE">natural numbers</a> set)</td><td rowspan="2">1895</td><td rowspan="3"><a href="/facts/Giuseppe_Peano/VT2Wsmu7">Giuseppe Peano</a></td></tr><tr><td> Q {\displaystyle \mathbb {Q} } </td><td><a href="/facts/Blackboard_bold/CGTmvA8H">Blackboard bold</a> capital Q (for <a href="/facts/Rational_number/VJQmyY05">rational numbers</a> set)</td></tr><tr><td>∃</td><td><a href="/facts/Existential_quantifier/hHveaBYo">existential quantifier</a> (<i>there exists</i>)</td><td>1897</td></tr><tr><td>·</td><td><a href="/facts/Middle_dot/FqdEx1gT">middle dot</a> (for <a href="/facts/Dot_product/tNz8MLjT">dot product</a>)</td><td rowspan="2">1902</td><td rowspan="2"><a href="/facts/J._Willard_Gibbs/xyWwxQtA">J. Willard Gibbs</a></td></tr><tr><td>×</td><td><a href="/facts/Multiplication_sign/XtsHgIbs">multiplication sign</a> (for <a href="/facts/Cross_product/uRBJzkcW">cross product</a>)</td></tr><tr><td>∨</td><td><a href="/facts/Logical_disjunction/jbI2EGlM">logical disjunction</a> (a.k.a. <i>OR</i>)</td><td>1906</td><td><a href="/facts/Bertrand_Russell/SRpwNX2U">Bertrand Russell</a></td></tr><tr><td>(...)</td><td rowspan="2"><a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> notation</td><td>1909</td><td><a href="/facts/Maxime_B%C3%B4cher/G0NfL4SJ">Maxime Bôcher</a></td></tr><tr><td>[...] </td><td>1909</td><td><a href="/facts/Gerhard_Kowalewski/wLCVxDQP">Gerhard Kowalewski</a></td></tr><tr><td>∮</td><td><a href="/facts/Line_integral/10s4B3Nn">contour integral</a> sign</td><td>1917</td><td><a href="/facts/Arnold_Sommerfeld/cJtpVHvn">Arnold Sommerfeld</a></td></tr><tr><td> Z {\displaystyle \mathbb {Z} } </td><td><a href="/facts/Blackboard_bold/CGTmvA8H">Blackboard bold</a> capital Z (for <a href="/facts/Integer/PUwwrawx">integer</a> numbers set)</td><td>1930</td><td><a href="/facts/Edmund_Landau/lVgFVLBw">Edmund Landau</a></td></tr><tr><td>∀</td><td><a href="/facts/Universal_quantifier/agNmvJKN">universal quantifier</a> (<i>for all</i>)</td><td>1935</td><td><a href="/facts/Gerhard_Gentzen/9ujN0ssI">Gerhard Gentzen</a></td></tr><tr><td rowspan="2">→</td><td rowspan="2"><a href="/facts/Arrow/B21BfJoL">arrow</a> (for <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> notation)</td><td>1936 (to denote images of specific elements)</td><td><a href="/facts/%C3%98ystein_Ore/mSpYnM3U">Øystein Ore</a></td></tr><tr><td>1940 (in the present form of <i>f</i>: <i>X</i> → <i>Y</i>)</td><td><a href="/facts/Witold_Hurewicz/oxcv63D2">Witold Hurewicz</a></td></tr><tr><td>∅</td><td><a href="/facts/Empty_set/ffEk3eA6">empty set</a> sign</td><td>1939</td><td><a href="/facts/Andr%C3%A9_Weil/Q4Dd0Gr4">André Weil</a> / <a href="/facts/Nicolas_Bourbaki/qRJhs9nr">Nicolas Bourbaki</a></td></tr><tr><td> C {\displaystyle \mathbb {C} } </td><td><a href="/facts/Blackboard_bold/CGTmvA8H">Blackboard bold</a> capital C (for <a href="/facts/Complex_number/2w7mqI7e">complex numbers</a> set)</td><td>1939</td><td><a href="/facts/Nathan_Jacobson/TEDrg4Lk">Nathan Jacobson</a></td></tr><tr><td>∎</td><td><a href="/facts/End_of_proof/5SuuaIrc">end of proof</a> sign (a.k.a. <a href="/facts/Tombstone_(typography)/5SuuaIrc">tombstone</a>)</td><td>1950</td><td><a href="/facts/Paul_Halmos/mR11lcap">Paul Halmos</a></td></tr><tr><td>⌊<i>x</i>⌋⌈<i>x</i>⌉</td><td><i>greatest integer ≤ x</i> (a.k.a. <a href="/facts/Floor_and_ceiling_functions/ssehyMMf">floor</a>) <i>smallest integer ≥ x</i> (a.k.a. <a href="/facts/Floor_and_ceiling_functions/ssehyMMf">ceiling</a>)</td><td>1962</td><td><a href="/facts/Kenneth_E._Iverson/2K4c4hsh">Kenneth E. Iverson</a></td></tr></tbody></table>