21、Binary Relations and Proximity Relations

Binary Relations and Proximity Relations

1 Introduction to Binary Relations

Binary relations are fundamental tools in mathematics and computer science, providing a framework to describe relationships between pairs of elements from two sets. In this article, we delve into the basics of binary relations and explore how they can be used to model various types of connections in computational geometry, topology, and digital image processing.

Key Concepts of Binary Relations

A binary relation ( R ) from set ( A ) to set ( B ) is a subset of the Cartesian product ( A \times B ). If ( (a, b) \in R ), we say that ( a ) is related to ( b ) by ( R ), denoted as ( aRb ).

Properties of Binary Relations

1. Reflexivity <