TeXipedia

emptyset

Denotes an empty set containing no elements, fundamental to set theory and mathematical notation.

Overview

Essential in mathematical logic, set theory, and formal proofs where the concept of a null or void collection is needed.

  • Commonly used in discrete mathematics to represent sets with zero elements
  • Appears frequently in computer science, particularly in algorithms and data structures
  • Critical in set operations and proofs involving subsets
  • Often used in conjunction with set builders and logical statements to define exclusion conditions

Examples

Defining a set with no elements

A=∅A = \emptyset 
A = \emptyset

Expressing that the intersection of disjoint sets is empty

A∩B=∅A \cap B = \emptyset 
A \cap B = \emptyset

Showing a solution set is empty for an impossible equation

{x∈R:x2+1=0}=∅\{x \in \mathbb{R} : x^2 + 1 = 0\} = \emptyset 
\{x \in \mathbb{R} : x^2 + 1 = 0\} = \emptyset