Symbols

156 of 156 entries

• α

  alpha

  Greek lowercase

  • A parameter, angle, fine-structure constant, or quantum amplitude.

  \alpha

  α|0⟩ + β|1⟩

• β

  beta

  Greek lowercase

  • A parameter, regression coefficient, beta particle, or quantum amplitude.

  \beta

  α|0⟩ + β|1⟩

• γ

  gamma

  Greek lowercase

  • The Lorentz factor, a gamma ray, or the Euler–Mascheroni constant.

  \gamma

  γ = 1 / √(1 − v²/c²)

• δ

  delta

  Greek lowercase

  • A small change, variation, or Dirac delta distribution.

  \delta

  δx

• ε

  epsilon

  Greek lowercase

  • A small quantity, permittivity, or error tolerance.

  \epsilon

  ε₀

• ζ

  zeta

  Greek lowercase

  • The Riemann zeta function or a damping ratio.

  \zeta

  ζ(s)

• η

  eta

  Greek lowercase

  • Efficiency, viscosity, or a learning rate.

  \eta

  η = useful output / input

• θ

  theta

  Greek lowercase

  • An angle, polar coordinate, or unknown model parameter.

  \theta

  sin θ

• ι

  iota

  Greek lowercase

  • A small index or the inclusion map in mathematics.

  \iota

  ι: A ↪ B

• κ

  kappa

  Greek lowercase

  • Curvature, thermal conductivity, or a condition number.

  \kappa

  κ

• λ

  lambda

  Greek lowercase

  • Wavelength, an eigenvalue, decay rate, or lambda-calculus function.

  \lambda

  λ = h/p

• μ

  mu (mew)

  Greek lowercase

  • The SI prefix micro (10⁻⁶), mean, friction coefficient, or reduced mass.

  \mu

  μm = 10⁻⁶ m

• ν

  nu (new)

  Greek lowercase

  • Frequency in physics; also used for neutrino flavours or degrees of freedom.

  \nu

  E = hν

• ξ

  xi (ksee)

  Greek lowercase

  • A random variable, correlation length, or spatial coordinate.

  \xi

  ξ

• ο

  omicron

  Greek lowercase

  • An ordinary Greek letter that is rarely used as a mathematical symbol.

  \omicron

  ο

• π

  pi

  Greek lowercase

  • The circle constant (about 3.14159…) or a product symbol when capitalised as Π.

  \pi

  C = 2πr

• ρ

  rho (row)

  Greek lowercase

  • Mass or charge density, correlation, or a quantum density matrix.

  \rho

  ρ = m/V

• σ

  sigma

  Greek lowercase

  • Standard deviation, cross-section, mechanical stress, or the Stefan–Boltzmann constant.

  \sigma

  σ = √variance

• τ

  tau

  Greek lowercase

  • A time constant, torque, proper time, or 2π.

  \tau

  τ = 2π

• υ

  upsilon

  Greek lowercase

  • A Greek letter used in particle names; rarely a standalone variable.

  \upsilon

  υ

• φ

  phi (fye)

  Greek lowercase

  • An angle, scalar field, potential, or phase.

  \phi

  φ(x)

• χ

  chi (kye)

  Greek lowercase

  • A chi-squared statistic, susceptibility, or character.

  \chi

  χ²

• ψ

  psi (sigh)

  Greek lowercase

  • A quantum wave function or state vector.

  \psi

  |ψ⟩

• ω

  omega

  Greek lowercase

  • Angular frequency; capital Ω also denotes ohms or solid angle.

  \omega

  ω = 2πf

• Α

  Alpha

  Greek uppercase

  • Uppercase Greek alpha; it looks like Latin A and is rarely used as a symbol.

  Α

• Β

  Beta

  Greek uppercase

  • Uppercase Greek beta; it looks like Latin B and is rarely used as a symbol.

  Β

• Γ

  Gamma

  Greek uppercase

  • The gamma function or a matrix of Dirac gamma matrices.

  \Gamma

  Γ(n)

• Δ

  Delta

  Greek uppercase

  • A finite change or difference; ∇² is the Laplacian, sometimes written Δ.

  \Delta

  Δx = x₂ − x₁

• Ε

  Epsilon

  Greek uppercase

  • Uppercase Greek epsilon; it looks like Latin E and is rarely used as a symbol.

  Ε

• Ζ

  Zeta

  Greek uppercase

  • Uppercase Greek zeta; it looks like Latin Z and is rarely used as a symbol.

  Ζ

• Η

  Eta

  Greek uppercase

  • Uppercase Greek eta; it looks like Latin H and is rarely used as a symbol.

  Η

• Θ

  Theta

  Greek uppercase

  • An angle or the asymptotic order notation Θ(n log n).

  \Theta

  T(n) = Θ(n log n)

• Ι

  Iota

  Greek uppercase

  • Uppercase Greek iota; it looks like Latin I and is rarely used as a symbol.

  Ι

• Κ

  Kappa

  Greek uppercase

  • Uppercase Greek kappa; it looks like Latin K and is rarely used as a symbol.

  Κ

• Λ

  Lambda

  Greek uppercase

  • An eigenvalue, cosmological constant, or lambda-particle symbol.

  \Lambda

  Av = λv

• Μ

  Mu

  Greek uppercase

  • Uppercase Greek mu; it looks like Latin M and is rarely used as a symbol.

  Μ

• Ν

  Nu

  Greek uppercase

  • Uppercase Greek nu; it looks like Latin N and is rarely used as a symbol.

  Ν

• Ξ

  Xi

  Greek uppercase

  • A Greek letter used for random variables, coordinates, and particle names.

  \Xi

  Ξ

• Ο

  Omicron

  Greek uppercase

  • Uppercase Greek omicron; it looks like Latin O and is rarely used as a symbol.

  Ο

• Π

  Pi

  Greek uppercase

  • Product notation, analogous to Σ for sums.

  \Pi

  ∏ᵢ₌₁ⁿ xᵢ

• Ρ

  Rho

  Greek uppercase

  • Uppercase Greek rho; it looks like Latin P and is rarely used as a symbol.

  Ρ

• Σ

  Sigma

  Greek uppercase

  • Summation; the lowercase σ has several meanings including standard deviation.

  \Sigma

  Σᵢ₌₁ⁿ xᵢ

• Τ

  Tau

  Greek uppercase

  • Uppercase Greek tau; it looks like Latin T and is rarely used as a symbol.

  Τ

• Υ

  Upsilon

  Greek uppercase

  • A Greek letter used in the name of the upsilon meson.

  \Upsilon

  Υ

• Φ

  Phi

  Greek uppercase

  • Magnetic flux, a scalar field, or a quantum state label.

  \Phi

  |Φ⁺⟩

• Χ

  Chi

  Greek uppercase

  • Uppercase Greek chi; it looks like Latin X and is rarely used as a symbol.

  Χ

• Ψ

  Psi

  Greek uppercase

  • A quantum state or wave function symbol.

  \Psi

  Ψ

• Ω

  Omega

  Greek uppercase

  • Electrical resistance in ohms or solid angle; also a sample space.

  \Omega

  R = 4 Ω

• +

  plus

  Operators

  • Addition; combine quantities.

  2 + 3 = 5

• −

  minus

  Operators

  • Subtraction or the negative sign; distinct from a hyphen.

  5 − 2 = 3

• ×

  times

  Operators

  • Multiplication, especially between numbers.

  \times

  3 × 4

• ·

  dot

  Operators

  • Multiplication or a scalar (dot) product.

  \cdot

  a · b

• ÷

  divided by

  Operators

  • Division.

  \div

  12 ÷ 3

• ±

  plus or minus

  Operators

  • Two possibilities: the positive and negative value.

  \pm

  x = 3 ± 1

• ∓

  minus or plus

  Operators

  • The paired opposite of ±, used in matching signs.

  \mp

  a ± b, c ∓ d

• =

  equals

  Relations

  • The expressions on both sides have the same value.

  \equals

  2 + 2 = 4

• ≠

  not equal

  Relations

  • The two values are different.

  \ne

  π ≠ 3

• ≈

  approximately equal

  Relations

  • The values are close, within an understood precision.

  \approx

  π ≈ 3.14159

• ≡

  identically equal / congruent

  Relations

  • An identity, or congruence modulo an integer.

  \equiv

  x² − 1 ≡ (x − 1)(x + 1)

• ∝

  proportional to

  Relations

  • One quantity is a constant multiple of another.

  \propto

  F ∝ 1/r²

• <

  less than

  Relations

  • The left value is smaller than the right value.

  \lt

  2 < 5

• >

  greater than

  Relations

  • The left value is larger than the right value.

  \gt

  5 > 2

• ≤

  less than or equal

  Relations

  • The left value is smaller than or equal to the right.

  \le

  x ≤ 10

• ≥

  greater than or equal

  Relations

  • The left value is larger than or equal to the right.

  \ge

  x ≥ 0

• ≪

  much less than

  Relations

  • The left scale is negligible compared with the right.

  \ll

  m ≪ M

• ≫

  much greater than

  Relations

  • The left scale is far larger than the right.

  \gg

  M ≫ m

• √

  square root

  Operators

  • The non-negative number whose square equals the input.

  \sqrt

  √9 = 3

• ∞

  infinity

  Constants

  • A concept of unbounded size, not an ordinary real number.

  \infty

  limₙ→∞

• ∑

  sum

  Operators

  • Summation over an indexed sequence.

  \sum

  ∑ᵢ₌₁ⁿ xᵢ

• ∏

  product

  Operators

  • Multiplication over an indexed sequence.

  \prod

  ∏ᵢ₌₁ⁿ xᵢ

• ∫

  integral

  Calculus

  • Accumulated quantity; area under a curve for a definite integral.

  \int

  ∫ₐᵇ f(x) dx

• ∮

  contour integral

  Calculus

  • An integral over a closed path or loop.

  \oint

  ∮ E · dl

• ∂

  partial derivative

  Calculus

  • Derivative with respect to one variable while holding others fixed.

  \partial

  ∂f/∂x

• ∇

  nabla / del

  Calculus

  • Vector differential operator; gives gradient, divergence or curl.

  \nabla

  ∇f

• d/dt

  derivative with respect to time

  Calculus

  • The rate of change of a quantity as time t changes.

  v = dx/dt

• ′

  prime

  Calculus

  • A derivative (f′), a new version of a variable, or arcminutes by context.

  \prime

  f′(x)

• →

  maps to / tends to

  Relations

  • A mapping, direction, or limiting behavior.

  \to, \rightarrow

  x → 0

• ⇒

  implies

  Relations

  • The statement on the left logically entails the one on the right.

  \Rightarrow, \Longrightarrow

  A ⇒ B

• ⇔

  if and only if

  Relations

  • Each statement implies the other; logical equivalence.

  \Leftrightarrow

  A ⇔ B

• ∀

  for all

  Sets & logic

  • Universal quantifier: a statement holds for every element.

  \forall

  ∀x ∈ ℝ

• ∃

  there exists

  Sets & logic

  • Existential quantifier: at least one element satisfies a statement.

  \exists

  ∃x: x² = 2

• ∈

  is an element of

  Sets & logic

  • The object belongs to a set.

  \in

  π ∈ ℝ

• ∉

  is not an element of

  Sets & logic

  • The object does not belong to a set.

  \notin

  π ∉ ℚ

• ⊂

  proper subset

  Sets & logic

  • Every element of the left set is in the right, and the sets differ.

  \subset

  ℕ ⊂ ℤ

• ⊆

  subset or equal

  Sets & logic

  • Every element of the left set is also in the right set.

  \subseteq

  A ⊆ B

• ∪

  union

  Sets & logic

  • The set of elements in either set.

  \cup

  A ∪ B

• ∩

  intersection

  Sets & logic

  • The set of elements shared by both sets.

  \cap

  A ∩ B

• ∅

  empty set

  Sets & logic

  • The set containing no elements.

  \emptyset

  A ∩ B = ∅

• ℕ

  natural numbers

  Sets & logic

  • The natural numbers; whether 0 is included depends on convention.

  \mathbb{N}

  1 ∈ ℕ

• ℤ

  integers

  Sets & logic

  • The positive and negative whole numbers and zero.

  \mathbb{Z}

  −3 ∈ ℤ

• ℚ

  rational numbers

  Sets & logic

  • Numbers expressible as a ratio of integers with nonzero denominator.

  \mathbb{Q}

  1/2 ∈ ℚ

• ℝ

  real numbers

  Sets & logic

  • All points on the continuous number line.

  \mathbb{R}

  √2 ∈ ℝ

• ℂ

  complex numbers

  Sets & logic

  • Numbers of the form a + bi with real a and b.

  \mathbb{C}

  i ∈ ℂ

• ¬

  not

  Sets & logic

  • Logical negation.

  \neg

  ¬A

• ∧

  and

  Sets & logic

  • Logical conjunction; both statements must hold.

  \land

  A ∧ B

• ∨

  or

  Sets & logic

  • Logical disjunction; at least one statement holds.

  \lor

  A ∨ B

• ⊕

  direct sum / exclusive or

  Sets & logic

  • Direct sum, or exclusive-or in logic; addition modulo 2 in quantum gates.

  \oplus

  a ⊕ b

• ⊗

  tensor product

  Quantum notation

  • Combines vector spaces or quantum systems.

  \otimes

  |0⟩ ⊗ |1⟩

• †

  dagger / Hermitian adjoint

  Quantum notation

  • Conjugate transpose of an operator or matrix.

  \dagger

  A†

• ⟨

  left angle bracket

  Quantum notation

  • Starts a bra vector or an inner product.

  \langle

  ⟨ψ|

• ⟩

  right angle bracket

  Quantum notation

  • Ends a ket vector or an inner product.

  \rangle

  |ψ⟩

• |ψ⟩

  ket

  Quantum notation

  • A quantum state vector in Dirac notation.

  \ket

  |ψ⟩

• ⟨ψ|

  bra

  Quantum notation

  • The dual vector of a ket; used to form inner products.

  \bra

  ⟨ψ|φ⟩

• ‖

  norm

  Operators

  • The length or magnitude of a vector; context determines the norm.

  \|

  ‖v‖

• |x|

  absolute value / magnitude

  Operators

  • Distance from zero on the number line; for complex x, its modulus.

  \lvert, \rvert

  |−3| = 3

• !

  factorial

  Operators

  • n! is the product of positive integers from 1 through n.

  5! = 120

• °

  degree

  Other

  • One 360th of a full turn, commonly used for angles and temperature.

  \degree

  90°

• ∠

  angle

  Other

  • Denotes an angle in geometry.

  \angle

  ∠ABC

• ⊥

  perpendicular

  Other

  • Two lines or vectors meet at a right angle.

  \perp

  a ⊥ b

• ∥

  parallel

  Other

  • Lines do not meet, or a parallel-vector relation.

  \parallel

  a ∥ b

• ∴

  therefore

  Other

  • Introduces a conclusion.

  \therefore

  a = b; ∴ b = a

• ∵

  because

  Other

  • Introduces a reason.

  \because

  ∵ a = b

• x̂

  x-hat

  Other

  • A unit vector, an estimated value, or an operator depending on context.

  \hat

  x̂

• x̄

  x-bar

  Other

  • The sample mean; in complex arithmetic, an overbar can mean complex conjugation.

  \bar

  x̄ = (x₁ + … + xₙ)/n

• ẋ

  x-dot

  Calculus

  • A dot over x denotes its time derivative in Newtonian mechanics.

  \dot

  ẋ = dx/dt

• ẍ

  x-double-dot

  Calculus

  • Two dots over x denote its second time derivative in Newtonian mechanics.

  \ddot

  ẍ = d²x/dt²

• *

  asterisk / convolution

  Operators

  • A context-dependent marker; often convolution, an adjoint in some fields, or multiplication.

  \ast

  f * g

• ℏ

  h-bar

  Constants

  • Reduced Planck constant h/(2π), about 1.054571817 × 10⁻³⁴ J·s.

  \hbar

  E = ℏω

• ħ

  h-bar (plain-text form)

  Constants

  • Reduced Planck constant h/(2π); the curly-bar character is ℏ.

  \hbar

  ħ = h/(2π)

• ℓ

  ell

  Other

  • Orbital angular-momentum quantum number or a length.

  \ell

  ℓ = 0, 1, 2, …

• e

  Euler's number / elementary charge

  Constants

  • Euler's number in calculus, or the elementary charge in physics; context matters.

  \mathrm{e}

  exp(x) = eˣ

• i

  imaginary unit

  Constants

  • The complex number with i² = −1; in physics it is often written j in engineering.

  \mathrm{i}

  eⁱπ + 1 = 0

• ∘

  composition / degree sign

  Operators

  • Function composition (f ∘ g); in other contexts, a circle or degree mark.

  \circ

  (f ∘ g)(x)

• mod

  modulo

  Operators

  • Remainder arithmetic or congruence with respect to a modulus.

  \bmod

  17 mod 5 = 2

• gcd

  greatest common divisor

  Operators

  • The largest positive integer dividing each of the given integers.

  \gcd

  gcd(12, 18) = 6

• Tr

  trace

  Operators

  • Sum of the diagonal entries of a square matrix.

  \operatorname{Tr}

  Tr(A)

• ln

  natural logarithm

  Operators

  • Logarithm to base e.

  \ln

  ln(e) = 1

• log

  logarithm

  Operators

  • A logarithm; the base is written or determined by convention.

  \log

  log₁₀(100) = 2

• exp

  exponential

  Operators

  • The exponential function, exp(x) = eˣ.

  \exp

  exp(0) = 1

• lim

  limit

  Calculus

  • The value a function approaches as its input approaches a value.

  \lim

  limₓ→₀ sin(x)/x = 1

• sin

  sine

  Operators

  • The trigonometric function giving the vertical coordinate on the unit circle.

  \sin

  sin(π/2) = 1

• cos

  cosine

  Operators

  • The trigonometric function giving the horizontal coordinate on the unit circle.

  \cos

  cos(0) = 1

• max

  maximum

  Operators

  • The greatest value in a set or range.

  \max

  max(x, y)

• ⋯

  midline ellipsis

  Other

  • Continuation of a sequence or a repeated series of centered terms.

  \cdots

  1 + 2 + ⋯ + n

• ⇌

  reversible reaction / equilibrium

  Relations

  • A reaction or process can proceed in either direction.

  \rightleftharpoons

  A ⇌ B

• ⁿ

  superscript n

  Other

  • A raised index commonly marks a power or a tensor index.

  xⁿ

• ₙ

  subscript n

  Other

  • A lowered index commonly labels a sequence member or component.

  aₙ

• 𝒟

  script D

  Quantum notation

  • A functional integration measure; in a path integral, 𝒟x denotes integration over paths.

  \mathcal{D}

  ∫ 𝒟x

• ϵ

  epsilon variant

  Greek lowercase

  • A common alternate handwritten or typeset form of lowercase epsilon.

  \epsilon

  ϵ₀

• ϑ

  theta variant

  Greek lowercase

  • An alternate form of lowercase theta, often used for a second angle.

  \vartheta

  ϑ

• ϕ

  phi variant

  Greek lowercase

  • An alternate form of lowercase phi.

  \varphi

  ϕ

• ς

  final sigma

  Greek lowercase

  • The word-final form of sigma; rarely used as a mathematical variable.

  \varsigma

  ς

• ϖ

  pi variant

  Greek lowercase

  • An alternate form of lowercase pi.

  \varpi

  ϖ

• ϱ

  rho variant

  Greek lowercase

  • An alternate form of lowercase rho.

  \varrho

  ϱ

• ⁺

  superscript plus

  Other

  • A raised plus sign, often indicating positive charge.

  \text{+}

  Na⁺

• ⁻

  superscript minus

  Other

  • A raised minus sign, often indicating negative charge or a negative exponent.

  \text{-}

  10⁻³

• ²

  superscript two

  Other

  • Square or second power.

  \text{2}

  x²

• ³

  superscript three

  Other

  • Cube or third power.

  \text{3}

  x³

• ⁴

  superscript four

  Other

  • Fourth power.

  \text{4}

  x⁴

• ᵘ

  superscript u

  Other

  • A raised u used as an index or exponent.

  γᵘ

• ₀

  subscript zero

  Other

  • A zero subscript often marks a reference or ground-state value.

  ε₀

• ₁

  subscript one

  Other

  • A first component or indexed quantity.

  x₁

• ₂

  subscript two

  Other

  • A second component or indexed quantity.

  x₂

• ₃

  subscript three

  Other

  • A third component or indexed quantity.

  x₃

• ₄

  subscript four

  Other

  • A fourth component or indexed quantity.

  x₄

• ↪

  injective map

  Sets & logic

  • An injective mapping or inclusion.

  \hookrightarrow

  A ↪ B