setminus
Denotes set difference or relative complement in set theory and mathematical notation.
Overview
Essential for expressing the removal or exclusion of elements from sets in mathematical contexts, particularly in set theory, discrete mathematics, and formal logic.
- Commonly used to show the elements that belong to one set but not another.
- Appears frequently in proofs and formal mathematical writing.
- Important in computer science for describing algorithms and data structures.
- Often encountered in topology and abstract algebra when working with subsets and group theory.
Examples
Showing the difference between two sets A and B.
A \setminus B = \{x \in A : x \notin B\}Expressing the complement of a subset.
\mathbb{R} \setminus \mathbb{Q} = \text{irrational numbers}Removing elements from a specific set.
\{1,2,3,4,5\} \setminus \{2,4\} = \{1,3,5\}