Mathematical Notations

Mathematical notation is a system of symbolic representations used for mathematical objects, operations, relations, and concepts. Here are some of the most commonly used notations:

Basic Operations

  • + : Addition
  • - : Subtraction
  • * or × : Multiplication
  • / or ÷ : Division
  • ^ or **: Exponentiation

Equality and Inequality

  • = : Equals
  • != or ≠ : Not equal to
  • < : Less than
  • > : Greater than
  • <= or ≤ : Less than or equal to
  • >= or ≥ : Greater than or equal to

Sets

  • {} : Set notation. Example: {1, 2, 3} is the set containing 1, 2, and 3.
  • ∈ : Element of. Example: 1 ∈ {1, 2, 3} means 1 is an element of the set {1, 2, 3}.
  • ∉ : Not an element of.
  • ∪ : Union of sets.
  • ∩ : Intersection of sets.
  • ⊆ : Subset of.
  • ⊂ : Proper subset of.
  • ⊇ : Superset of.
  • ⊃ : Proper superset of.
  • ∅ : The empty set.

Functions

  • f(x) : Function notation. f is the function, and x is the input to the function.

Calculus

  • d/dx : Derivative of a function with respect to x.
  • ∫ : Integral symbol.
  • ∆ : Delta, often used to represent a small change in a variable.
  • ∂ : Partial derivative symbol.
  • ∞ : Infinity.

Summation and Product

  • Σ : Summation symbol. Σ_{i=1}^{n} a_i represents the sum of a_i from i=1 to n.
  • Π : Product symbol. Π_{i=1}^{n} a_i represents the product of a_i from i=1 to n.

Logic

  • ∧ : Logical AND.
  • ∨ : Logical OR.
  • ¬ : Logical NOT.
  • → : Logical implication.
  • ↔ : Logical equivalence.

Other Symbols

  • ∃ : There exists.
  • ∀ : For all.
  • ≈ : Approximately equal to.
  • ∝ : Proportional to.

Remember that the use of these symbols can vary between different branches of mathematics and different texts.