Math Symbols List (+,-,x,/,=,...) (2024)

List of all mathematical symbols and signs - meaning and examples.

SymbolSymbol NameMeaning / definitionExample=equals signequality5 = 2+3
5 is equal to 2+3≠not equal signinequality5 ≠ 4
5 is not equal to 4≈approximately equalapproximationsin(0.01) ≈ 0.01,
xy means x is approximately equal to y>strict inequalitygreater than5 > 4
5 is greater than 4<strict inequalityless than4 < 5
4 is less than 5≥inequalitygreater than or equal to5 ≥ 4,
xymeans x is greater than or equal to y≤inequalityless than or equal to4 ≤ 5,
x ≤ y means xis less than or equal to y( )parenthesescalculate expression inside first 2 × (3+5) = 16[ ]bracketscalculate expression inside first [(1+2)×(1+5)] = 18+plus signaddition1 + 1 = 2−minus signsubtraction2 − 1 = 1±plus - minusboth plus and minus operations3 ± 5 = 8 or -2±minus - plusboth minus and plus operations3 ∓ 5 = -2 or 8*asteriskmultiplication2 * 3 = 6×times signmultiplication2 × 3 = 6⋅multiplication dotmultiplication2 ⋅ 3 = 6÷division sign / obelusdivision6 ÷ 2 = 3/division slashdivision6 / 2 = 3—horizontal linedivision / fractionMath Symbols List (+,-,x,/,=,...) (1)modmoduloremainder calculation7 mod 2 = 1.perioddecimal point, decimal separator2.56 = 2+56/100abpowerexponent23 = 8a^bcaretexponent2 ^ 3 = 8√asquare root

aa = a

9 = ±33acube root3a3a 3a = a38 = 24afourth root4a4a 4a 4a =a416 = ±2nan-th root (radical)for n=3, n8 = 2%percent1% = 1/10010% × 30 = 3‰per-mille1‰ = 1/1000 = 0.1%10‰ × 30 = 0.3ppmper-million1ppm = 1/100000010ppm × 30 = 0.0003ppbper-billion1ppb = 1/100000000010ppb × 30 = 3×10-7pptper-trillion1ppt = 10-1210ppt × 30 = 3×10-10
SymbolSymbol NameMeaning / definitionExample∠angleformed by two rays∠ABC = 30°Math Symbols List (+,-,x,/,=,...) (2)measured angleMath Symbols List (+,-,x,/,=,...) (3)ABC = 30°Math Symbols List (+,-,x,/,=,...) (4)spherical angleMath Symbols List (+,-,x,/,=,...) (5)AOB = 30°∟right angle= 90°α = 90°°degree1 turn = 360°α = 60°degdegree1 turn = 360degα = 60deg′primearcminute, 1° = 60′α = 60°59′″double primearcsecond, 1′ = 60″α = 60°59′59″Math Symbols List (+,-,x,/,=,...) (6)lineinfinite lineABline segmentline from point A to point BMath Symbols List (+,-,x,/,=,...) (7)rayline that start from point AMath Symbols List (+,-,x,/,=,...) (8)arcarc from point A to point BMath Symbols List (+,-,x,/,=,...) (9) = 60°⊥perpendicularperpendicular lines (90° angle)ACBC&par;parallelparallel linesAB &par; CD≅congruent toequivalence of geometric shapes and size∆ABC≅ ∆XYZ~similaritysame shapes, not same size∆ABC~ ∆XYZΔtriangletriangle shapeΔABC≅ ΔBCD|x-y|distancedistance between points x and y| x-y | = 5πpi constantπ = 3.141592654...

is the ratio between the circumference and diameter of a circle

c = πd = 2⋅πrradradiansradians angle unit360° = 2π radcradiansradians angle unit360° = 2π cgradgradians / gonsgrads angle unit360° = 400 gradggradians / gonsgrads angle unit360° = 400 g
SymbolSymbol NameMeaning / definitionExamplexx variableunknown value to findwhen 2x = 4, then x = 2≡equivalenceidentical to≜equal by definitionequal by definition:=equal by definitionequal by definition~approximately equalweak approximation11 ~ 10≈approximately equalapproximationsin(0.01) ≈ 0.01∝proportional toproportional to

yx when y = kx, k constant

lemniscateinfinity symbol≪much less thanmuch less than1 ≪ 1000000≫much greater thanmuch greater than1000000 ≫ 1( )parenthesescalculate expression inside first 2 * (3+5) = 16[ ]bracketscalculate expression inside first [(1+2)*(1+5)] = 18{ }bracesset⌊x⌋floor bracketsrounds number to lower integer⌊4.3⌋ = 4⌈x⌉ceiling bracketsrounds number to upper integer⌈4.3⌉ = 5x!exclamation markfactorial4! = 1*2*3*4 = 24| x |vertical barsabsolute value| -5 | = 5f (x)function of xmaps values of x to f(x)f (x) = 3x+5(fg)function composition(fg) (x) = f (g(x))f (x)=3x,g(x)=x-1⇒(fg)(x)=3(x-1)(a,b)open interval(a,b) = {x | a < x < b}x∈ (2,6)[a,b]closed interval[a,b] = {x | axb}x ∈ [2,6]∆deltachange / difference∆t = t1 - t0∆discriminantΔ = b2 - 4ac∑sigmasummation - sum of all values in range of series∑ xi= x1+x2+...+xn∑∑sigmadouble summationMath Symbols List (+,-,x,/,=,...) (10)∏capital piproduct - product of all values in range of series∏ xi=x1∙x2∙...∙xnee constant/ Euler's numbere = 2.718281828...e = lim (1+1/x)x, x→∞γEuler-Mascheroni constantγ = 0.5772156649...φgolden ratiogolden ratio constantπpi constantπ = 3.141592654...

is the ratio between the circumference and diameter of a circle

c = πd = 2⋅πr
SymbolSymbol NameMeaning / definitionExample·dotscalar producta · b×crossvector producta × bABtensor producttensor product of A and BABMath Symbols List (+,-,x,/,=,...) (11)inner product[ ]bracketsmatrix of numbers( )parenthesesmatrix of numbers| A |determinantdeterminant of matrix Adet(A)determinantdeterminant of matrix A || x ||double vertical barsnormATtransposematrix transpose(AT)ij = (A)jiAHermitian matrixmatrix conjugate transpose(A)ij = (A)jiA*Hermitian matrixmatrix conjugate transpose(A*)ij =(A)jiA-1inverse matrixA A-1 = Irank(A)matrix rankrank of matrix Arank(A) = 3dim(U)dimensiondimension of matrix Adim(U) = 3
SymbolSymbol NameMeaning / definitionExampleP(A)probability functionprobability of event AP(A) = 0.5P(AB)probability of events intersectionprobability that of events A and BP(AB) = 0.5P(AB)probability of events unionprobability that of events A or BP(AB) = 0.5P(A | B)conditional probability functionprobability of event A given event B occuredP(A | B) = 0.3f (x)probability density function (pdf)P(a x b) = ∫ f (x) dxF(x)cumulative distribution function (cdf)F(x) = P(X x)μpopulation meanmean of population valuesμ = 10E(X)expectation valueexpected value of random variable XE(X) = 10E(X | Y)conditional expectationexpected value of random variable X given YE(X | Y=2) = 5var(X)variancevariance of random variable Xvar(X) = 4σ2variancevariance of population valuesσ2 = 4std(X)standard deviationstandard deviation of random variable Xstd(X) = 2σXstandard deviationstandard deviation value of random variable XσX = 2Math Symbols List (+,-,x,/,=,...) (12)medianmiddle value of random variable xMath Symbols List (+,-,x,/,=,...) (13)cov(X,Y)covariancecovariance of random variables X and Ycov(X,Y) = 4corr(X,Y)correlationcorrelation of random variables X and Ycorr(X,Y) = 0.6ρX,Ycorrelationcorrelation of random variables X and YρX,Y= 0.6∑summationsummation - sum of all values in range of seriesMath Symbols List (+,-,x,/,=,...) (14)∑∑double summationdouble summationMath Symbols List (+,-,x,/,=,...) (15)Momodevalue that occurs most frequently in populationMRmid-rangeMR = (xmax+xmin)/2Mdsample medianhalf the population is below this valueQ1lower / first quartile25% of population are below this valueQ2median / second quartile50% of population are below this value = median of samplesQ3upper / third quartile75% of population are below this valuexsample meanaverage / arithmetic mean x = (2+5+9) / 3 = 5.333s 2sample variancepopulation samples variance estimators 2 = 4ssample standard deviation population samples standard deviation estimators = 2zxstandard scorezx = (x-x)/ sxX ~distribution of Xdistribution of random variable XX ~ N(0,3) N(μ,σ2)normal distributiongaussian distributionX ~ N(0,3) U(a,b)uniform distributionequal probability in range a,b X ~ U(0,3) exp(λ)exponential distributionf (x) = λe-λx , x≥0gamma(c, λ)gamma distributionf (x) = λ c xc-1e-λx/ Γ(c), x≥0χ 2(k)chi-square distributionf (x) = xk/2-1e-x/2/ ( 2k/2 Γ(k/2) )F (k1, k2)F distribution Bin(n,p)binomial distributionf (k) = nCk pk(1-p)n-k Poisson(λ)Poisson distributionf (k) = λke-λ / k! Geom(p)geometric distributionf (k) = p(1-p) k HG(N,K,n)hyper-geometric distributionBern(p)Bernoulli distribution
SymbolSymbol NameMeaning / definitionExamplen!factorialn! = 1⋅2⋅3⋅...⋅n5! = 1⋅2⋅3⋅4⋅5 = 120nPkpermutationMath Symbols List (+,-,x,/,=,...) (16)5P3 =5! / (5-3)! = 60nCk

Math Symbols List (+,-,x,/,=,...) (17)

combinationMath Symbols List (+,-,x,/,=,...) (18)5C3 =5!/[3!(5-3)!]=10
SymbolSymbol NameMeaning / definitionExample{ }seta collection of elementsA = {3,7,9,14},
B = {9,14,28}A ∩ Bintersectionobjects that belong to set A and set BA ∩ B = {9,14}A ∪ Bunionobjects that belong to set A or set BA ∪ B = {3,7,9,14,28}A ⊆ BsubsetA is a subset of B. set A is included in set B.{9,14,28} ⊆ {9,14,28}A ⊂ Bproper subset / strict subsetA is a subset of B, but A is not equal to B.{9,14} ⊂ {9,14,28}A ⊄ Bnot subsetset A is not a subset of set B{9,66} ⊄ {9,14,28}A ⊇ BsupersetA is a superset of B. set A includes set B{9,14,28} ⊇ {9,14,28}A ⊃ Bproper superset / strict supersetA is a superset of B, but B is not equal to A.{9,14,28} ⊃ {9,14}A ⊅ Bnot supersetset A is not a superset of set B{9,14,28} ⊅ {9,66}2Apower setall subsets of AMath Symbols List (+,-,x,/,=,...) (19)power setall subsets of AA = Bequalityboth sets have the same membersA={3,9,14},
B={3,9,14},
A=BAccomplementall the objects that do not belong to set AA \ Brelative complementobjects that belong to A and not to BA = {3,9,14},
B = {1,2,3},
A-B = {9,14}A - Brelative complementobjects that belong to A and not to BA = {3,9,14},
B = {1,2,3},
A-B = {9,14}A ∆ Bsymmetric differenceobjects that belong to A or B but not totheir intersectionA = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}A ⊖ Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14}a∈Aelement of,
belongs toset membershipA={3,9,14}, 3 ∈ Ax∉Anot element ofno set membershipA={3,9,14}, 1 ∉ A(a,b)ordered paircollection of 2 elementsA×Bcartesian productset of all ordered pairs from A and BA×B = {(a,b)|a∈A , b∈B}|A|cardinalitythe number of elements of set AA={3,9,14}, |A|=3#Acardinalitythe number of elements of set AA={3,9,14}, #A=3|vertical barsuch thatA={x|3<x<14}Math Symbols List (+,-,x,/,=,...) (20)aleph-nullinfinite cardinality of natural numbers setMath Symbols List (+,-,x,/,=,...) (21)aleph-onecardinality of countable ordinal numbers setØempty setØ = { }C = {Ø}Math Symbols List (+,-,x,/,=,...) (22)universal setset of all possible valuesMath Symbols List (+,-,x,/,=,...) (23)0natural numbers / whole numbers set (with zero)Math Symbols List (+,-,x,/,=,...) (24)0 = {0,1,2,3,4,...}0 ∈ Math Symbols List (+,-,x,/,=,...) (25)0Math Symbols List (+,-,x,/,=,...) (26)1natural numbers / whole numbers set (without zero)Math Symbols List (+,-,x,/,=,...) (27)1 = {1,2,3,4,5,...}6 ∈ Math Symbols List (+,-,x,/,=,...) (28)1Math Symbols List (+,-,x,/,=,...) (29)integer numbers setMath Symbols List (+,-,x,/,=,...) (30) = {...-3,-2,-1,0,1,2,3,...}-6 ∈ Math Symbols List (+,-,x,/,=,...) (31)Math Symbols List (+,-,x,/,=,...) (32)rational numbers setMath Symbols List (+,-,x,/,=,...) (33) = {x | x=a/b,a,bMath Symbols List (+,-,x,/,=,...) (34)}2/6 ∈ Math Symbols List (+,-,x,/,=,...) (35)Math Symbols List (+,-,x,/,=,...) (36)real numbers setMath Symbols List (+,-,x,/,=,...) (37) = {x | -∞ < x <∞}6.343434∈Math Symbols List (+,-,x,/,=,...) (38)Math Symbols List (+,-,x,/,=,...) (39)complex numbers setMath Symbols List (+,-,x,/,=,...) (40) = {z | z=a+bi, -∞<a<∞, -∞<b<∞}6+2iMath Symbols List (+,-,x,/,=,...) (41)
SymbolSymbol NameMeaning / definitionExampleandandx y^caret / circumflexandx ^ y&ampersandandx & y+plusorx + y∨reversed caretorxy|vertical lineorx | yx'single quotenot - negationx'xbarnot - negationx¬notnot - negation¬ x!exclamation marknot - negation! x⊕circled plus / oplusexclusive or - xorxy~tildenegation~ x⇒implies⇔equivalentif and only if (iff)↔equivalentif and only if (iff)∀for all∃there exists∄there does not exists∴therefore∵because / since
SymbolSymbol NameMeaning / definitionExampleMath Symbols List (+,-,x,/,=,...) (42)limitlimit value of a functionεepsilonrepresents a very small number, near zeroε 0ee constant / Euler's numbere = 2.718281828...e = lim (1+1/x)x , x→∞y 'derivativederivative - Lagrange's notation(3x3)' = 9x2y ''second derivativederivative of derivative(3x3)'' = 18xy(n)nth derivativen times derivation(3x3)(3) = 18Math Symbols List (+,-,x,/,=,...) (43)derivativederivative - Leibniz's notationd(3x3)/dx = 9x2Math Symbols List (+,-,x,/,=,...) (44)second derivativederivative of derivatived2(3x3)/dx2 = 18xMath Symbols List (+,-,x,/,=,...) (45)nth derivativen times derivationMath Symbols List (+,-,x,/,=,...) (46)time derivativederivative by time - Newton's notationMath Symbols List (+,-,x,/,=,...) (47)time second derivativederivative of derivativeDx yderivativederivative - Euler's notationDx2ysecond derivativederivative of derivativeMath Symbols List (+,-,x,/,=,...) (48)partial derivative∂(x2+y2)/∂x = 2xintegralopposite to derivation∫ f(x)dx∫∫double integralintegration of function of 2 variables∫∫ f(x,y)dxdy∫∫∫triple integralintegration of function of 3 variables∫∫∫ f(x,y,z)dxdydz∮closed contour / line integral∯closed surface integral∰closed volume integral[a,b]closed interval[a,b] = {x | a x b}(a,b)open interval(a,b) = {x | a < x < b}iimaginary uniti ≡ √-1z = 3 + 2iz*complex conjugatez = a+biz*=a-biz* = 3 - 2izcomplex conjugatez = a+biz =a-biz = 3 - 2iRe(z)real part of a complex numberz = a+bi → Re(z)=aRe(3 - 2i) = 3Im(z)imaginary part of a complex numberz = a+bi → Im(z)=bIm(3 - 2i) = -2| z |absolute value/magnitude of a complex number|z| = |a+bi| = &Sqrt;(a2+b2)|3 - 2i| = &Sqrt;13arg(z)argument of a complex numberThe angle of the radius in the complex planearg(3 + 2i) = 33.7°∇nabla / delgradient / divergence operator∇f (x,y,z)Math Symbols List (+,-,x,/,=,...) (49)vectorMath Symbols List (+,-,x,/,=,...) (50)unit vectorx * yconvolutiony(t) = x(t) * h(t)Math Symbols List (+,-,x,/,=,...) (51)Laplace transformF(s) = Math Symbols List (+,-,x,/,=,...) (52){f (t)}Math Symbols List (+,-,x,/,=,...) (53)Fourier transformX(ω) = Math Symbols List (+,-,x,/,=,...) (54){f (t)}δdelta function∞lemniscateinfinity symbol
NameWestern ArabicRomanEastern ArabicHebrewzero0٠one1I١אtwo2II٢בthree3III٣גfour4IV٤דfive5V٥הsix6VI٦וseven7VII٧זeight8VIII٨חnine9IX٩טten10X١٠יeleven11XI١١יאtwelve12XII١٢יבthirteen13XIII١٣יגfourteen14XIV١٤ידfifteen15XV١٥טוsixteen16XVI١٦טזseventeen17XVII١٧יזeighteen18XVIII١٨יחnineteen19XIX١٩יטtwenty20XX٢٠כthirty30XXX٣٠לforty40XL٤٠מfifty50L٥٠נsixty60LX٦٠סseventy70LXX٧٠עeighty80LXXX٨٠פninety90XC٩٠צone hundred100C١٠٠ק
Upper Case LetterLower Case LetterGreek Letter NameEnglish Equivalent Letter Name PronounceΑαAlphaaal-faΒβBetabbe-taΓγGammagga-maΔδDeltaddel-taΕεEpsiloneep-si-lonΖζZetazze-taΗηEtaheh-taΘθThetathte-taΙιIotaiio-taΚκKappakka-paΛλLambdallam-daΜμMumm-yooΝνNunnooΞξXixx-eeΟοOmicronoo-mee-c-ronΠπPippa-yeeΡρRhorrowΣσSigmassig-maΤτTautta-ooΥυUpsilonuoo-psi-lonΦφPhiphf-eeΧχChichkh-eeΨψPsipsp-seeΩωOmegaoo-me-ga
NumberRoman numeral0not defined1I2II3III4IV5V6VI7VII8VIII9IX10X11XI12XII13XIII14XIV15XV16XVI17XVII18XVIII19XIX20XX30XXX40XL50L60LX70LXX80LXXX90XC100C200CC300CCC400CD500D600DC700DCC800DCCC900CM1000M5000V10000X50000L100000C500000D1000000M
Math Symbols List (+,-,x,/,=,...) (2024)

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