What Does the Notation = in Equivalence Classes Conclude to?

Click For Summary
SUMMARY

The discussion focuses on the notation "=" in equivalence classes, specifically addressing the property (a) that concludes to [a]=[m]. The user questions whether it should instead be represented as [a]⊆[m], similar to the relationship [m]⊆M. The notation ##a \in [m]## is explored, along with the implications of transitivity in the relation ##\sim## for elements ##b \sim a## and ##c \sim m##. The conversation clarifies the distinctions between equivalence classes and their subsets.

PREREQUISITES
  • Understanding of equivalence relations and classes
  • Familiarity with set notation and properties
  • Knowledge of transitive relations in mathematics
  • Basic grasp of mathematical logic and notation
NEXT STEPS
  • Study the properties of equivalence relations in detail
  • Learn about set theory, focusing on subset relations
  • Explore transitivity in mathematical relations
  • Review examples of equivalence classes in various mathematical contexts
USEFUL FOR

Students of mathematics, educators teaching set theory, and anyone interested in the foundations of equivalence relations and their applications.

kidsasd987
Messages
142
Reaction score
4
Please refer to the video at 37:02 from the link above.

I am struggling with the notation "=" of the property (a) which concludes to [a]=[m].
shouldn't it be [a]⊆[m], just like [m]⊆M.
 
Physics news on Phys.org
What does ##a \in [m]## mean? And what can be said about all elements ##b \sim a## if we use transitivity of ##\sim##?
In retrun, what does it mean for all elements ##c \sim m##?
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 29 ·
Replies
29
Views
6K
  • · Replies 14 ·
Replies
14
Views
6K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 36 ·
2
Replies
36
Views
6K