Example: Examples of Equivalence Relations

(related to Definition: Equivalence Relation)

It is easy to verify the reflexivity, symmetry and transitivity of the following properties. Thus, all these properties are equivalence relations. 1. Equality of numbers 1. Parallelity of straight lines in the plane 1. Sets having the same cardinality. 1. Similarity of shapes in the plane. Two shapes in a plane are said to be similar if one can be transformed into another by a combination of enlargements, reflections, translations or rotations. The similarity of shapes is an equivalence class. The following figure shows two similar shapes.


5. Some cleverly chosen equivalence relations can be used to define integers, rational numbers, and real numbers.

  1. Integers having the same modulus.
  2. Connectivity of graphs
  3. Subspaces of vector spaces
  4. Subspaces of vector spaces

Thank you to the contributors under CC BY-SA 4.0!