List of mathematical symbols - Basic Knowledge 101

1 List of mathematical symbolsThis is a list of symbols used in all branches of mathematics to express a formula or to represent a mathematical concept is independent of the symbol chosen to represent it. For many of the symbols below, the symbol is usually synonymous with the corresponding concept (ultimately an arbitrarychoice made as a result of the cumulative history of mathematics), but in some situations, a different convention may be used. For example, depending on context, the triple bar " " may representcongruence or a definition. However, in mathematical logic, numerical equality is sometimes represented by " " instead of "=", with the latter representing equality of well-formed formulas. In short,convention dictates the symbol is shown both in HTML, whose display depends on the browser's access to an appropriate font installed on the particular device, and typeset as an image using symbolsSymbols based on equalitySymbols that point left or rightBracketsOther non-letter symbolsLetter-based symbolsLetter modifiersSymbols based on Latin lettersSymbols based on Hebrew or Greek lettersVariationsSee alsoReferencesExternal linksThis list is organized by symbol type and is intended to facilitate finding an unfamiliar symbol by its visual appearance.

2 For a related list organized by mathematical topic, see List of mathematicalsymbols by subject. That list also includes LaTeX and HTML markup, and Unicode code points for each symbol (note that this article doesn't have the latter two, but they could certainly be added).There is a Wikibooks guide for using maths in LaTeX,[1] and a comprehensive LaTeX symbol list.[2] It is also possible to check to see if a Unicode code point is available as a LaTeX command, or viceversa.[3] Also note that where there is no LaTeX command natively available for a particular symbol (although there may be options that require adding packages), the symbol could be added via otheroptions, such as setting the document up to support Unicode,[4] and entering the character in a variety of ways ( copying and pasting, keyboard shortcuts, the \unicode{<insertcodepoint>}command[5]) as well as other options[6] and extensive additional information.

3 [7][8] Basic symbols : symbols widely used in mathematics, roughly through first-year calculus. More advanced meanings are included with some symbols listed based on equality "=": symbols derived from or similar to the equal sign, including double-headed arrows. Not surprisingly these symbols are often associated with anequivalence that point left or right: symbols , such as < and >, that appear to point to one side or : symbols that are placed on either side of a variable or expression, such as |x|.Other non-letter symbols : symbols that do not fall in any of the other symbols : Many mathematical symbols are based on, or closely resemble, a letter in some alphabet. This section includes such symbols , including symbols thatresemble upside-down letters. Many letters have conventional meanings in various branches of mathematics and physics.

4 These are not listed here. The See also section, below,has several lists of such modifiers: symbols that can be placed on or next to any letter to modify the letter's based on Latin letters, including those symbols that resemble or contain an XSymbols based on Hebrew or Greek letters , , , , , , , , . Note: symbols resembling are grouped with "V" under Latin : Usage in languages written right-to-leftContentsGuideBasic symbolsSymbol in HTMLS ymbol in TeXNameExplanationExamplesRead asCategory+additionplus; addarithmetic4 + 6 means the sum of 4 and + 7 = 9disjoint unionthe disjointunion of ..and ..set theoryA1 + A2 means the disjoint union ofsets A1 and = {3, 4, 5, 6} A2 = {7, 8, 9, 10} A1 + A2 = {(3, 1), (4, 1), (5, 1), (6, 1), (7, 2), (8, 2), (9, 2), (10, 2)} subtractionminus; take; subtractarithmetic36 11 means the subtraction of 11from 11 = 25negative signnegative; minus; the oppositeofarithmetic 3 means the additive inverse of thenumber 3.

5 ( 5) = 5set-theoreticcomplementminus; withoutset theoryA B means the set that contains allthe elements of A that are not in B. ( can also be used for set-theoreticcomplement as described below.){1, 2, 4} {1, 3, 4} = {2} \pmplus-minusplus or minusarithmetic6 3 means both 6 + 3 and 6 equation x = 5 4, has two solutions, x = 7 and x = or minusmeasurement10 2 or equivalently 10 20%means the range from 10 2 to10 + a = 100 1 mm, then a 99 mm and a 101 mm. \mpminus-plusminus or plusarithmetic6 (3 5) means 6 + (3 5) and6 (3 + 5).cos(x y) = cos(x) cos(y) sin(x) sin(y). \times \cdotmultiplicationtimes; multiplied byarithmetic3 4 or 3 4 means the multiplicationof 3 by 8 = 56dot productscalar productdotlinear algebravectoralgebrau v means the dot product of vectorsu and v(1, 2, 5) (3, 4, 1) = 6cross productvectorproductcrosslinear algebravectoralgebrau v means the cross product ofvectors u and v(1, 2, 5) (3, 4, 1) = ijk12534 1 = ( 22, 16, 2)placeholder(silent)functionalanalysisA means a placeholder for anargument of a function.

6 Indicates thefunctional nature of an expressionwithout assigning a specific symbol foran argument.| | \div division(Obelus)divided by; overarithmetic6 3 or 6 3 means the division of 6by 4 = 12 4 = 3quotientgroupmodgroup theoryG / H means the quotient of group Gmodulo its subgroup H.{0, a, 2a, b, b + a, b + 2a} / {0, b} = {{0, b}, {a, b + a}, {2a, b + 2a}}quotient setmodset theoryA/~ means the set of all ~ equivalenceclasses in we define ~ by x ~ y x y , then /~ = {x + n : n , x [0,1)}. \surd \sqrt{x}square root(radicalsymbol)the (principal)square root ofreal numbers x means the nonnegative numberwhose square is x. 4 = 2complexsquare rootthe (complex)square root ofcomplexnumbersIf z = r exp(i ) is represented in polarcoordinates with < , then z = r exp(i /2).]

7 1 = i summation\sumsum over ..from .. to ..ofcalculus means . \intindefiniteintegral orantiderivativeindefiniteintegral of - OR - theantiderivativeofcalculus f(x) dx means a function whosederivative is to .. of ..with respecttocalculus f(x) dx means the signed areabetween the x-axis and the graph of thefunction f between x = a and x = b. x2 dx = b3 a33line integralline/ path/curve/ integralof .. along ..calculus f ds means the integral of f alongthe curve C, f(r(t)) |r'(t)| dt, wherer is a parametrization of C. (If the curveis closed, the symbol may be usedinstead, as described below.) \ointContourintegral; closed lineintegralcontourintegral ofcalculusSimilar to the integral, but used todenote a single integration over aclosed curve or loop. It is sometimesused in physics texts involvingequations regarding Gauss's Law, andwhile these formulas involve a closedsurface integral, the representationsdescribe only the first integration of thevolume over the enclosing where the latter requiressimultaneous double integration, thesymbol would be more third related symbol is the closedvolume integral, denoted by the contour integral can also frequentlybe found with a subscript capital letterC, C, denoting that a closed loopintegral is, in fact, around a contour C,or sometimes dually appropriately, acircle C.

8 In representations of Gauss'sLaw, a subscript capital S, S, is usedto denote that the integration is over aclosed C is a Jordan curve about 0, then C 1z dz = 2 \ldots \cdots \vdots \ddotsellipsisand so fortheverywhereIndicates omitted values from a + 1/4 + 1/8 + 1/16 + = 1 \thereforethereforetherefore; so; henceeverywhereSometimes used in proofs beforelogical humans are mortal. Socrates is a human. Socrates is mortal. \becausebecausebecause; sinceeverywhereSometimes used in proofs is prime it has no positive integer factors other than itself and one.!factorialfactorialcombinatorics means the product .logicalnegationnotpropositionallogicThe statement !A is true if and only if Ais false. A slash placed through anotheroperator is the same as "!" placed infront.

9 (The symbol ! is primarily fromcomputer science. It is avoided inmathematical texts, where the notation A is preferred.)!(!A) A x y !(x = y) b a b a C b a \neg logicalnegationnotpropositionallogicThe statement A is true if and only if Ais false. A slash placed through anotheroperator is the same as " " placed infront. (The symbol ~ has many other uses, so or the slash notation is scientists will often use ! butthis is avoided in mathematical texts.) ( A) A x y (x = y) \proptoproportionalityis proportionalto; varies aseverywherey x means that y = kx for someconstant y = 2x, then y x. \inftyinfinityinfinitynumbers is an element of the extendednumber line that is greater than all realnumbers; it often occurs in limits. \blacksquare \Box \blacktrianglerightend of proofQED; tombstone; Halmosfinality symboleverywhereUsed to mark the end of a proof.

10 (May also be written ) symbols based on equalitySymbol in HTMLS ymbol in TeXNameExplanationExamplesRead asCategory=equalityis equal to; equalseverywhere means and represent the same thing or value. \neinequalityis not equal to; does not equaleverywhere means that and do not represent the same thing or value. (The forms !=, /= or <> are generally used in programminglanguages where ease of typing and use of ASCII text is preferred.) \approxapproximatelyequalis approximatelyequal toeverywherex y means x is approximately equal to y. This may also be written , , ~, (Libra Symbol), or . isomorphic togroup theoryG H means that group G is isomorphic (structurally identical) togroup H. ( can also be used for isomorphic, as described below.)Q8 / C2 V~ \simprobabilitydistributionhas distributionstatisticsX ~ D, means the random variable X has the probability ~ N(0,1), the standardnormal distributionrow equivalenceis row equivalenttomatrix theoryA ~ B means that B can be generated by using a series ofelementary row operations on Asame order ofmagnituderoughly similar; poorlyapproximates; is on the order ofapproximationtheorym ~ n means the quantities m and n have the same order ofmagnitude, or general size.