TeXipedia

O

Represents the empty set or null set in mathematical notation, indicating a collection containing no elements.

Overview

Essential in set theory and mathematical logic for denoting the absence of elements in a set. Commonly appears in:

  • Set theory proofs and definitions
  • Computer science and logic programming
  • Database theory when describing null results
  • Mathematical statements involving complements and intersections

Particularly important in foundational mathematics and formal reasoning where precise notation for emptiness is required.

Examples

Indicating an empty or null set in mathematical notation.

A∩B=ØA \cap B = \text{\O} 
A \cap B = \text{\O}

Showing that a collection contains no elements.

{x∈R:x2<0}=Ø\{x \in \mathbb{R} : x^2 < 0\} = \text{\O} 
\{x \in \mathbb{R} : x^2 < 0\} = \text{\O}

Expressing the complement of a universal set in set theory.

Uc=ØU^c = \text{\O} 
U^c = \text{\O}