What are all of the mathematical symbols?

Answer 1

=equals signequality5 = 2+3≠not equal signinequality5 ≠ 4>strict inequalitygreater than5 > 4a bpowerexponent23 = 8a^bcaretexponent2 ^ 3 = 8√asquare root

√a · √a = a√9 = ±33√acube root3√8 = 24√aforth root4√16 = ±2n√an-th root (radical)for n=3, n√8 = 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-trillion1ppb = 10-1210ppb × 30 = 3×10-10

Geometry symbolsSymbolSymbol NameMeaning / definitionExample∠angleformed by two rays

∠ABC = 30º∡measured angle∡ABC = 30º∢spherical angle∢AOB = 30º∟right angle= 90ºα = 90ººdegree1 turn = 360ºα = 60º´arcminute1º = 60´α = 60º59'´´arcsecond1´ = 60´´α = 60º59'59''ABlineline from point A to point Brayline that start from point A|perpendicularperpendicular lines (90º angle)AC | BCparallelparallel linesAB 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 circlec = π·d = 2·π·rradradiansradians angle unit360º = 2π radgradgradsgrads angle unit360º = 400 grad

Algebra symbolsSymbolSymbol 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

f(x) ∝ g(x)∞lemniscateinfinity symbol≪much less thanmuch less than1 ≪ 1000000≫much greater thanmuch greater than1000000 ≫ 1( )parenthesescalculate expression inside first2 * (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 |single vertical barabsolute value| -5 | = 5f (x)function of xmaps values of x to f(x)f(x) = 3x+5(f ∘g)function composition

(f ∘g) (x) = f(g(x))f (x)=3x, g(x)=x-1 ⇒(f∘g)(x)=3(x-1)(a,b)open interval(a,b) ≜ {x | a < x< b}x ∈ (2,6)[a,b]closed interval[a,b] ≜ {x | a ≤ x ≤ b}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 summation∏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 = 0.527721566...φgolden ratiogolden ratio constant

Linear Algebra SymbolsSymbolSymbol NameMeaning / definitionExample∙dotscalar producta ∙ b×crossvector producta × bA⊗Btensor producttensor product of A and BA ⊗ Binner product[ ]bracketsmatrix of numbers( )parenthesesmatrix of numbers| A |determinantdeterminant of matrix Adet(A)determinantdeterminant of matrix A xdouble vertical barsnormA Ttransposematrix transpose

(AT)ij = (A)jiA †Hermitian 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 A

rank(A) = 3dim(U)dimensiondimension of matrix A

rank(U) = 3

Probability and statistics symbolsSymbolSymbol NameMeaning / definitionExampleP(A)probability functionprobability of event AP(A) = 0.5P(A ∩ B)probability of events intersectionprobability that of events A and BP(A∩B) = 0.5P(A ∪ B)probability of events unionprobability that of events A or BP(A∪B) = 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= 2medianmiddle value of random variable xcov(X,Y)covariancecovariance of random variables X and Ycov(X,Y) = 4corr(X,Y)correlationcorrelation of random variables X and Ycorr(X,Y) = 3ρX,Ycorrelationcorrelation of random variables X and YρX,Y = 3∑summationsummation - sum of all values in range of series∑∑double summationdouble summationMomodevalue that occurs most frequently in populationMRmid-range

MR = (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 meanx = (2+5+9) / 3 = 5.333s 2sample variancepopulation samples variance estimators 2 = 4ssample standard deviationpopulation samples standard deviation estimators = 2zxstandard score

zx = (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,bX ~ U(0,3)exp(λ)exponential distributionf(x) = λe-λx , x≥0gamma(c, λ)gamma distribution

f (x) = λ c xc-1e-λx / Γ(c), x≥0χ 2(k)chi-square distribution

f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) )F (k1, k2)F distributionBin(n,p)binomial distribution

f (k) = nCk pk(1-p)n-kPoisson(λ)Poisson distribution

f (k) = λke-λ / k!Geom(p)geometric distribution

f (k) = p(1-p) kHG(N,K,n)hyper-geometric distributionBern(p)Bernoulli distribution

Combinatorics SymbolsSymbolSymbol NameMeaning / definitionExamplen!factorialn! = 1·2·3·...·n5! = 1·2·3·4·5 = 120nPkpermutation5P3 = 5! / (5-3)! = 60nCk

combination5C3 = 5!/[3!(5-3)!]=10

Set theory symbolsSymbolSymbol 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 ⊆ Bsubsetsubset has less elements or equal to the set{9,14,28} ⊆ {9,14,28}A ⊂ Bproper subset / strict subsetsubset has less elements than the set{9,14} ⊂ {9,14,28}A ⊄ Bnot subsetleft set not a subset of right set{9,66} ⊄ {9,14,28}A ⊇ Bsupersetset A has more elements or equal to the set B{9,14,28} ⊇ {9,14,28}A ⊃ Bproper superset / strict supersetset A has more elements than set B{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 AƤ (A)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 to their 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 ofset 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 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=3אalephinfinite cardinalityØempty setØ = { }C = {Ø}Uuniversal setset of all possible valuesℕ0natural numbers / whole numbers set (with zero)ℕ0 = {0,1,2,3,4,...}0 ∈ ℕ0ℕ1natural numbers / whole numbers set (without zero)ℕ1 = {1,2,3,4,5,...}6 ∈ ℕ1ℤinteger numbers setℤ = {...-3,-2,-1,0,1,2,3,...}-6 ∈ ℤℚrational numbers setℚ = {x | x=a/b, a,b∈ℕ}2/6 ∈ ℚℝreal numbers setℝ = {x | -∞ < x <∞}6.343434 ∈ ℝℂcomplex numbers setℂ = {z | z=a+bi, -∞<a<∞, -∞<b<∞}6+2i ∈ ℂ Logic symbolsSymbolSymbol NameMeaning / definitionExample·andand

x · y^caret / circumflexand

x ^ y&ersandand

x & y+plusor

x + y∨reversed caretor

x ∨ y|vertical lineor

x | yx'single quotenot - negation

x'xbarnot - negation

x¬notnot - negation

¬ x!exclamation marknot - negation

! x⊕circled plus / oplusexclusive or - xor

x ⊕ y~tildenegation

~ x⇒implies⇔equivalentif and only if∀for all∃there exists∄there does not exists∴therefore∵because / since

Calculus & analysis symbolsSymbolSymbol NameMeaning / definitionExamplelimitlimit value of a functionεepsilonrepresents a very small number, near zero

ε → 0ee constant / Euler's numbere = 2.718281828...e = lim (1+1/x)x , x→∞y 'derivativederivative - Leibniz's notation(3x3)' = 9x2y ''second derivativederivative of derivative(3x3)'' = 18xy(n)nth derivativen times derivation(3x3)(3) = 18derivativederivative - Lagrange's notationd(3x3)/dx = 9x2second derivativederivative of derivatived2(3x3)/dx2 = 18xnth derivativen times derivationtime derivativederivative by time - Newton notationtime second derivativederivative of derivativepartial derivative∂(x2+y2)/∂x = 2x∫integralopposite to derivation∬double integralintegration of function of 2 variables∭triple integralintegration of function of 3 variables∮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+bi → z*=a-biz* = 3 + 2izcomplex conjugatez = a+bi → z = a-biz = 3 + 2i∇nabla / delgradient / divergence operator∇f(x,y,z)vectorunit vectorx * yconvolutiony(t) = x(t) * h(t)ℒLaplace transformF(s) = ℒ{f(t)}ℱFourier transformX(ω) = ℱ{f(t)}δdelta function

Numeral symbolsNameEuropeanRomanHindu ArabicHebrewzero0٠one1I١אtwo2II٢בthree3III٣גfour4IV٤דfive5V٥הsix6VI٦וseven7VII٧זeight8VIII٨חnine9IX٩טten10X١٠יeleven11XI١١יאtwelve12XII١٢יבthirteen13XIII١٣יגfourteen14XIV١٤ידfifteen15XV١٥טוsixteen16XVI١٦טזseventeen17XVII١٧יזeighteen18XVIII١٨יחnineteen19XIX١٩יטtwenty20XX٢٠כthirty30XXX٣٠לfourty40XL٤٠מfifty50L٥٠נsixty60LX٦٠סseventy70LXX٧٠עeighty80LXXX٨٠פninety90XC٩٠צone hundred100C١٠٠ק Greek alphabet lettersGreek SymbolGreek Letter NameEnglish EquivalentPronunciationUpper CaseLower CaseΑαAlphaaal-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 Roman numeralsNumberRoman numeral1I2II3III4IV5V6VI7VII8VIII9IX10X11XI12XII13XIII14XIV15XV16XVI17XVII18XVIII19XIX20XX30XXX40XL50L60LX70LXX80LXXX90XC100C200CC300CCC400CD500D600DC700DCC800DCCC900CM1000M5000V10000X50000L100000C500000D1000000M