Here’s a comprehensive list of common mathematical symbols along with their meanings:
Basic Arithmetic Symbols
- + (plus): Addition
- − (minus): Subtraction
- × or ∙ (times or dot): Multiplication
- ÷ or / (division or slash): Division
- = (equals): Equality
- ≠ (not equal): Inequality
- < (less than)
- > (greater than)
- ≤ (less than or equal to)
- ≥ (greater than or equal to)
Algebraic Symbols
- a, b, c, x, y, z, …: Variables
- n: Usually an integer
- i: The imaginary unit (√−1)
- π (pi): Approximately 3.14159, the ratio of a circle’s circumference to its diameter
- e: Euler’s number, approximately 2.71828
- √ (square root)
- ∛ (cube root)
- x², x³, x⁴, …: Powers of x
- |x|: Absolute value of x
Functions and Operators
- f(x): Function of x
- sin, cos, tan: Sine, cosine, tangent functions
- ln(x): Natural logarithm of x
- log(x): Logarithm of x (commonly base 10)
- exp(x): Exponential function (e^x)
- ∑ (sigma): Summation
- ∏ (pi): Product
Set Theory Symbols
- ∈: Element of
- ∉: Not an element of
- ⊂: Proper subset
- ⊆: Subset
- ⊄: Not a subset
- ∪: Union
- ∩: Intersection
- ∅: Empty set
- |A|: Cardinality of set A
- ℕ: Set of natural numbers
- ℤ: Set of integers
- ℚ: Set of rational numbers
- ℝ: Set of real numbers
- ℂ: Set of complex numbers
Logic Symbols
- ¬: Not
- ∧: And
- ∨: Or
- →: Implies
- ↔: If and only if (iff)
- ∀: For all (universal quantifier)
- ∃: There exists (existential quantifier)
- ⊥: Contradiction (false)
- ⊢: Entails
- ⊨: Satisfies
Calculus Symbols
- d: Differential
- ∫: Integral
- ∂: Partial derivative
- Δ: Change in (difference)
- ∞: Infinity
- lim: Limit
Probability and Statistics Symbols
- P(A): Probability of event A
- E(X): Expected value of X
- Var(X): Variance of X
- σ: Standard deviation
- μ: Mean
- ρ or r: Correlation coefficient
- X ~ N(μ, σ²): X is normally distributed with mean μ and variance σ²
Matrix and Vector Symbols
- A, B, C, …: Matrices
- I: Identity matrix
- 0: Zero matrix
- T: Transpose
- det(A): Determinant of matrix A
- A⁻¹: Inverse of matrix A
- x, y, z, …: Vectors
- ||x||: Norm of vector x
- a · b: Dot product
- a × b: Cross product
Miscellaneous Symbols
- !: Factorial
- ∴: Therefore
- ∵: Because
- ∠: Angle
- ⊥: Perpendicular
- ||: Parallel
- ∂/∂x: Partial derivative with respect to x
- ℓ: Length
This is a broad overview, and many fields of mathematics have their own specific symbols. If you need more detailed information on any particular area or symbol, feel free to ask!