Mathematical Notation Reference¶

A quick reference for common mathematical symbols and notation.

Greek Letters¶

Symbol	Name	Usage/Meaning
α	alpha	Angles, coefficients, significance level
β	beta	Angles, regression coefficients, type II error
γ	gamma	Euler's constant, Lorentz factor
δ	delta	Change, Dirac delta, Kronecker delta
ε	epsilon	Small positive quantity (ε-δ proofs)
ζ	zeta	Riemann zeta function
η	eta	Efficiency, partial correlation
θ	theta	Angles, parameters
λ	lambda	Eigenvalues, wavelength, Poisson rate
μ	mu	Mean, population mean
ν	nu	Degrees of freedom, frequency
π	pi	3.14159..., circle constant
ρ	rho	Correlation coefficient, density
σ	sigma	Standard deviation, sum symbol (Σ)
τ	tau	Torque, 2π
φ	phi	Golden ratio (1.618...), Euler's totient
χ	chi	Chi-squared distribution
ψ	psi	Wave function, digamma function
ω	omega	Angular frequency, complex cube root
Σ	Sigma (capital)	Summation
Π	Pi (capital)	Product
Δ	Delta (capital)	Change, discriminant
Ω	Omega (capital)	Sample space, Ohm

Symbol	Name	Usage/Meaning
∈	Element of	x ∈ S — x is in set S
∉	Not element of	x ∉ S — x is not in set S
⊂	Subset	A ⊂ B — A is a subset of B
⊆	Subset or equal	A ⊆ B — A is a subset of or equal to B
∪	Union	A ∪ B — elements in A or B
∩	Intersection	A ∩ B — elements in A and B
∅	Empty set	Set with no elements
\	Set difference	A \ B — elements in A not in B
×	Cartesian product	A × B — ordered pairs (a, b)
ℕ	Natural numbers	{0, 1, 2, 3, ...}
ℤ	Integers	{..., -2, -1, 0, 1, 2, ...}
ℚ	Rational numbers	Fractions p/q
ℝ	Real numbers	All numbers on the number line
ℂ	Complex numbers	a + bi

Symbol	Name	Usage/Meaning
∧	And (conjunction)	P ∧ Q — P and Q
∨	Or (disjunction)	P ∨ Q — P or Q
¬	Not (negation)	¬P — not P
→	Implication	P → Q — if P then Q
↔	Biconditional	P ↔ Q — P if and only if Q
∀	For all	∀x P(x) — for all x, P(x) holds
∃	There exists	∃x P(x) — there exists x such that P(x)
∴	Therefore	Conclusion indicator
⊢	Turnstile	Logical entailment
⊨	Double turnstile	Semantic entailment

Symbol	Name	Usage/Meaning
=	Equals	a = b — a equals b
≠	Not equal	a ≠ b — a does not equal b
≈	Approximately	a ≈ b — a is approximately b
≡	Identical to	a ≡ b (mod n) — congruence
<	Less than	a < b
>	Greater than	a > b
≤	Less than or equal	a ≤ b
≥	Greater than or equal	a ≥ b
≪	Much less than	a ≪ b
≫	Much greater than	a ≫ b
∝	Proportional to	a ∝ b — a = kb
∼	Similar to	Distribution, equivalence relation

Symbol	Name	Usage/Meaning
dx	Differential of x	Infinitesimal change in x
dy/dx	Derivative	Derivative of y with respect to x
d²y/dx²	Second derivative	Second derivative of y
∂	Partial derivative	∂f/∂x — partial derivative
∫	Integral	∫ f(x) dx — indefinite integral
∫_a^b	Definite integral	∫_a^b f(x) dx — integral from a to b
∮	Contour integral	Integral around a closed curve
lim	Limit	lim_{x→a} f(x) — limit as x approaches a
→	Approaches	x → a — x approaches a
∞	Infinity	Unbounded quantity
∇	Nabla (gradient)	∇f — gradient vector field
Δ	Laplacian	Δf = ∇²f — sum of second partials