What is the Difference Between Factor Space and Equivalence Classes?

Click For Summary
SUMMARY

The discussion clarifies that factor space, denoted as S/R, represents the set of equivalence classes defined by an equivalence relation R. This concept is distinct from equivalence classes themselves, which are the individual subsets formed by the relation R. The reference to page 8 of "A Course in Modern Mathematical Physics" by Szekeres provides additional context for understanding these definitions. The distinction is crucial for grasping advanced mathematical concepts in physics.

PREREQUISITES
  • Understanding of equivalence relations in mathematics
  • Familiarity with set theory concepts
  • Basic knowledge of mathematical physics
  • Ability to interpret mathematical notation
NEXT STEPS
  • Study the properties of equivalence relations in detail
  • Explore the concept of quotient sets in set theory
  • Read "A Course in Modern Mathematical Physics" by Szekeres for deeper insights
  • Investigate applications of factor spaces in physics
USEFUL FOR

Mathematicians, physics students, and educators seeking to deepen their understanding of factor spaces and equivalence classes in mathematical contexts.

commutator
Messages
12
Reaction score
0
FACTOR SPACE is defined in my book as the set whose elements are the equivalence classes defined by the equivalence relation R .denoted by S/R

i cannot understand where this is different from equivalent class?
page 8 - a coursein modern mathematical physics - szekeres
any help will be highly appreciated.
 
Last edited:
Physics news on Phys.org
understood. thanks.
 

Similar threads

Undergrad Localising a non integral domain at a prime
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Example of a factor space in physics
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Meaning of "passage to the quotient"?
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Factor (Quotient) Space definitions.
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Definition of minimal ideal using symbolic logic notation
  • · Replies 3 ·
Replies
3
Views
2K
Courses Math Course Advice -- Harvard freshman planning to double major in physics and mathematics
  • · Replies 41 ·
2
Replies
41
Views
9K
MHB Glad I could help! Good luck with your studies.
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Homemorphism in quotient topology
  • · Replies 5 ·
Replies
5
Views
2K
Graduate About computing the tangent space at 1 of certain lie groups
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Understanding Co-vectors to Dual Spaces and Linear Functionals
  • · Replies 6 ·
Replies
6
Views
3K