# Basic Math Symbols (Algebra Geometry Statistics etc.)

## Basic math symbols

 Symbol Symbol Name Meaning / definition Example = equals sign equality 5 = 2+3 5 is equal to 2+3 ≠ not equal sign inequality 5 ≠ 4 5 is not equal to 4 ≈ approximately equal approximation sin(0.01) ≈ 0.01, x ≈ y means x is approximately equal to y > strict inequality greater than 5 > 4 5 is greater than 4 < strict inequality less than 4 < 5 4 is less than 5 ≥ inequality greater than or equal to 5 ≥ 4, x ≥ y means x is greater than or equal to y ≤ inequality less than or equal to 4 ≤ 5, x ≤ y means x is greater than or equal to y ( ) parentheses calculate expression inside first 2 × (3+5) = 16 [ ] brackets calculate expression inside first [(1+2)×(1+5)] = 18 + plus sign addition 1 + 1 = 2 − minus sign subtraction 2 − 1 = 1 ± plus – minus both plus and minus operations 3 ± 5 = 8 and -2 ± minus – plus both minus and plus operations 3 ± 5 = -2 and 8 * asterisk multiplication 2 * 3 = 6 × times sign multiplication 2 × 3 = 6 · multiplication dot multiplication 2 · 3 = 6 ÷ division sign / obelus division 6 ÷ 2 = 3 / division slash division 6 / 2 = 3 – horizontal line division / fraction mod modulo remainder calculation 7 mod 2 = 1 . period decimal point, decimal separator 2.56 = 2+56/100 ab power exponent 23 = 8 a^b caret exponent 2 ^ 3 = 8 √a square root √a · √a  = a √9 = ±3 3√a cube root 3√a · 3√a  · 3√a  = a 3√8 = 2 4√a fourth root 4√a · 4√a  · 4√a  · 4√a  = a 4√16 = ±2 n√a n-th root (radical) for n=3, n√8 = 2 % percent 1% = 1/100 10% × 30 = 3 ‰ per-mille 1‰ = 1/1000 = 0.1% 10‰ × 30 = 0.3 ppm per-million 1ppm = 1/1000000 10ppm × 30 = 0.0003 ppb per-billion 1ppb = 1/1000000000 10ppb × 30 = 3×10-7 ppt per-trillion 1ppt = 10-12 10ppt × 30 = 3×10-10

## Algebra symbols

 Symbol Symbol Name Meaning / definition Example x x variable unknown value to find when 2x = 4, then x = 2 ≡ equivalence identical to ≜ equal by definition equal by definition := equal by definition equal by definition ~ approximately equal weak approximation 11 ~ 10 ≈ approximately equal approximation sin(0.01) ≈ 0.01 ∝ proportional to proportional to y ∝ x when y = kx, k constant ∞ lemniscate infinity symbol ≪ much less than much less than 1 ≪ 1000000 ≫ much greater than much greater than 1000000 ≫ 1 ( ) parentheses calculate expression inside first 2 * (3+5) = 16 [ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18 { } braces set ⌊x⌋ floor brackets rounds number to lower integer ⌊4.3⌋ = 4 ⌈x⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉ = 5 x! exclamation mark factorial 4! = 1*2*3*4 = 24 | x | single vertical bar absolute value | -5 | = 5 f (x) function of x maps 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] ∆ delta change / difference ∆t = t1 – t0 ∆ discriminant Δ = b2 – 4ac ∑ sigma summation – sum of all values in range of series ∑ xi= x1+x2+…+xn ∑∑ sigma double summation ∏ capital pi product – product of all values in range of series ∏ xi=x1∙x2∙…∙xn e e constant / Euler’s number e = 2.718281828… e = lim (1+1/x)x , x→∞ γ Euler-Mascheroni  constant γ = 0.527721566… φ golden ratio golden ratio constant π pi constant π = 3.141592654…is the ratio between the circumference and diameter of a circle c = π·d = 2·π·r

## Linear Algebra Symbols

 Symbol Symbol Name Meaning / definition Example · dot scalar product a · b × cross vector product a × b A⊗B tensor product tensor product of A and B A ⊗ B inner product [ ] brackets matrix of numbers ( ) parentheses matrix of numbers | A | determinant determinant of matrix A det(A) determinant determinant of matrix A || x || double vertical bars norm AT transpose matrix transpose (AT)ij = (A)ji A† Hermitian matrix matrix conjugate transpose (A†)ij = (A)ji A* Hermitian matrix matrix conjugate transpose (A*)ij = (A)ji A -1 inverse matrix A A-1 = I rank(A) matrix rank rank of matrix A rank(A) = 3 dim(U) dimension dimension of matrix A rank(U) = 3

## Probability and statistics symbols

 Symbol Symbol Name Meaning / definition Example P(A) probability function probability of event A P(A) = 0.5 P(A ∩ B) probability of events intersection probability that of events A and B P(A∩B) = 0.5 P(A ∪ B) probability of events union probability that of events A or B P(A∪B) = 0.5 P(A | B) conditional probability function probability of event A given event B occured P(A | B) = 0.3 f (x) probability density function (pdf) P(a ≤ x ≤ b) = ∫ f (x) dx F(x) cumulative distribution function (cdf) F(x) = P(X≤ x) μ population mean mean of population values μ = 10 E(X) expectation value expected value of random variable X E(X) = 10 E(X | Y) conditional expectation expected value of random variable X given Y E(X | Y=2) = 5 var(X) variance variance of random variable X var(X) = 4 σ2 variance variance of population values σ2 = 4 std(X) standard deviation standard deviation of random variable X std(X) = 2 σX standard deviation standard deviation value of random variable X σX  = 2 median middle value of random variable x cov(X,Y) covariance covariance of random variables X and Y cov(X,Y) = 4 corr(X,Y) correlation correlation of random variables X and Y corr(X,Y) = 0.6 ρX,Y correlation correlation of random variables X and Y ρX,Y = 0.6 ∑ summation summation – sum of all values in range of series ∑∑ double summation double summation Mo mode value that occurs most frequently in population MR mid-range MR = (xmax+xmin)/2 Md sample median half the population is below this value Q1 lower / first quartile 25% of population are below this value Q2 median / second quartile 50% of population are below this value = median of samples Q3 upper / third quartile 75% of population are below this value x sample mean average / arithmetic mean x = (2+5+9) / 3 = 5.333 s 2 sample variance population samples variance estimator s 2 = 4 s sample standard deviation population samples standard deviation estimator s = 2 zx standard score zx = (x–x) / sx X ~ distribution of X distribution of random variable X X ~ N(0,3) N(μ,σ2) normal distribution gaussian distribution X ~ N(0,3) U(a,b) uniform distribution equal probability in range a,b X ~ U(0,3) exp(λ) exponential distribution f (x) = λe–λx , x≥0 gamma(c, λ) gamma distribution f (x) = λ c xc-1e–λx / Γ(c), x≥0 χ 2(k) chi-square distribution f (x) = xk/2-1e–x/2 / ( 2k/2 Γ(k/2) ) F (k1, k2) F distribution Bin(n,p) binomial distribution f (k) = nCk pk(1-p)n-k Poisson(λ) Poisson distribution f (k) = λke–λ / k! Geom(p) geometric distribution f (k) =  p(1-p) k HG(N,K,n) hyper-geometric distribution Bern(p) Bernoulli distribution

## Combinatorics Symbols

 Symbol Symbol Name Meaning / definition Example n! factorial n! = 1·2·3·…·n 5! = 1·2·3·4·5 = 120 nPk permutation 5P3 = 5! / (5-3)! = 60 nCk combination 5C3 = 5!/[3!(5-3)!]=10

## Set theory symbols

 Symbol Symbol Name Meaning / definition Example { } set a collection of elements A = {3,7,9,14}, B = {9,14,28} A ∩ B intersection objects that belong to set A and set B A ∩ B = {9,14} A ∪ B union objects that belong to set A or set B A ∪ B = {3,7,9,14,28} A ⊆ B subset subset has fewer elements or equal to the set {9,14,28} ⊆ {9,14,28} A ⊂ B proper subset / strict subset subset has fewer elements than the set {9,14} ⊂ {9,14,28} A ⊄ B not subset left set not a subset of right set {9,66} ⊄ {9,14,28} A ⊇ B superset set A has more elements or equal to the set B {9,14,28} ⊇ {9,14,28} A ⊃ B proper superset / strict superset set A has more elements than set B {9,14,28} ⊃ {9,14} A ⊅ B not superset set A is not a superset of set B {9,14,28} ⊅ {9,66} 2A power set all subsets of A power set all subsets of A A = B equality both sets have the same members A={3,9,14}, B={3,9,14}, A=B Ac complement all the objects that do not belong to set A A \ B relative complement objects that belong to A and not to B A = {3,9,14}, B = {1,2,3}, A-B = {9,14} A – B relative complement objects that belong to A and not to B A = {3,9,14}, B = {1,2,3}, A-B = {9,14} A ∆ B symmetric difference objects that belong to A or B but not to their intersection A = {3,9,14}, B = {1,2,3}, A ∆ B = {1,2,9,14} A ⊖ B symmetric difference objects that belong to A or B but not to their intersection A = {3,9,14}, B = {1,2,3}, A ⊖ B = {1,2,9,14} a∈A element of set membership A={3,9,14}, 3 ∈ A x∉A not element of no set membership A={3,9,14}, 1 ∉ A (a,b) ordered pair collection of 2 elements A×B cartesian product set of all ordered pairs from A and B |A| cardinality the number of elements of set A A={3,9,14}, |A|=3 #A cardinality the number of elements of set A A={3,9,14}, #A=3 aleph-null infinite cardinality of natural numbers set aleph-one cardinality of countable ordinal numbers set Ø empty set Ø = { } C = {Ø} universal set set of all possible values 0 natural numbers / whole numbers  set (with zero) 0 = {0,1,2,3,4,…} 0 ∈  0 1 natural numbers / whole numbers  set (without zero) 1 = {1,2,3,4,5,…} 6 ∈  1 integer numbers set = {…-3,-2,-1,0,1,2,3,…} -6 ∈ rational numbers set = {x | x=a/b, a,b∈ } 2/6 ∈ real numbers set = {x | -∞ < x <∞} 6.343434∈ complex numbers set = {z | z=a+bi, -∞

## Logic symbols

 Symbol Symbol Name Meaning / definition Example · and and x · y ^ caret / circumflex and x ^ y & ampersand and x & y + plus or x + y ∨ reversed caret or x ∨ y | vertical line or x | y x‘ single quote not – negation x‘ x bar not – negation x ¬ not not – negation ¬ x ! exclamation mark not – negation ! x ⊕ circled plus / oplus exclusive or – xor x ⊕ y ~ tilde negation ~ x ⇒ implies ⇔ equivalent if and only if (iff) ↔ equivalent if and only if (iff) ∀ for all ∃ there exists ∄ there does not exists ∴ therefore ∵ because / since

## Calculus & analysis symbols

 Symbol Symbol Name Meaning / definition Example limit limit value of a function ε epsilon represents a very small number, near zero ε → 0 e e constant / Euler’s number e = 2.718281828… e = lim (1+1/x)x ,x→∞ y ‘ derivative derivative – Lagrange’s notation (3x3)’ = 9x2 y ” second derivative derivative of derivative (3x3)” = 18x y(n) nth derivative n times derivation (3x3)(3) = 18 derivative derivative – Leibniz’s notation d(3x3)/dx = 9x2 second derivative derivative of derivative d2(3x3)/dx2 = 18x nth derivative n times derivation time derivative derivative by time – Newton’s notation time second derivative derivative of derivative Dx y derivative derivative – Euler’s notation Dx2y second derivative derivative of derivative partial derivative ∂(x2+y2)/∂x = 2x ∫ integral opposite to derivation ∫ f(x)dx ∫∫ double integral integration of function of 2 variables ∫∫ f(x,y)dxdy ∫∫∫ triple integral integration 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} i imaginary unit i ≡ √-1 z = 3 + 2i z* complex conjugate z = a+bi → z*=a–bi z* = 3 – 2i z complex conjugate z = a+bi → z = a–bi z = 3 – 2i ∇ nabla / del gradient / divergence operator ∇f (x,y,z) vector unit vector x * y convolution y(t) = x(t) * h(t) Laplace transform F(s) = {f (t)} Fourier transform X(ω) =  {f (t)} δ delta function ∞ lemniscate infinity symbol

## Greek alphabet letters

 Greek Symbol Greek Letter Name English Equivalent Pronunciation Upper Case Lower Case Α α Alpha a al-fa Β β Beta b be-ta Γ γ Gamma g ga-ma Δ δ Delta d del-ta Ε ε Epsilon e ep-si-lon Ζ ζ Zeta z ze-ta Η η Eta h eh-ta Θ θ Theta th te-ta Ι ι Iota i io-ta Κ κ Kappa k ka-pa Λ λ Lambda l lam-da Μ μ Mu m m-yoo Ν ν Nu n noo Ξ ξ Xi x x-ee Ο ο Omicron o o-mee-c-ron Π π Pi p pa-yee Ρ ρ Rho r row Σ σ Sigma s sig-ma Τ τ Tau t ta-oo Υ υ Upsilon u oo-psi-lon Φ φ Phi ph f-ee Χ χ Chi ch kh-ee Ψ ψ Psi ps p-see Ω ω Omega o o-me-ga
SHARE
Previous articleIslamiat