Fundamental Theorem of Equivalence Relation and Congruence Modulo M | Group Theory | CSIR NET Maths
In Fundamental Theorem of Equivalence Relation & Congruence Modulo M in Group Theory Lecture 4 (III) by Dubey Sir, the session focuses on two central topics: the fundamental theorem of equivalence relations and the concept of congruence modulo m within group theory. Dubey Sir begins by revisiting the idea of an equivalence relation, a relation that satisfies reflexivity, symmetry, and transitivity. He explains the Fundamental Theorem of Equivalence Relations, which states that every equivalence relation on a set results in a partition of that set into disjoint equivalence classes. This concept is crucial for understanding how mathematical structures can be broken down into simpler, well-defined subsets.
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📚 Topics Covered:
Fundamental Theorem of Equivalence Relation
Example
Congruence Modulo M
Results and Properties (1)
Results and Properties (2)
Quotient Set
Residue Class
Properties
Note & Example
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This video is about;
What is the equivalence relation theorem?
What is congruent modulo m?
What is the congruence modulo equation?
What is the quotient set in group theory?
What is the symbol for the quotient set?
What is a quotient set example?
Is a quotient set a partition?
What is meant by residue class?
Congruence modulo m is an equivalence relation
Congruence modulo examples
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