Equivalence Classes: Decomposition and Quotient Set

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Explores equivalence relations, reflexivity, equivalence classes, and constructing new sets based on equivalent elements.

Introduces equivalence classes for decomposing a set into subsets of equivalent elements, defining the quotient set X/~.

Covers equivalence classes, relations, quotient sets, and functions properties.

Covers the concept of Kähler differentials, exploring linearity, construction, and B-linearity in algebraic geometry.

Covers bases, transformations, and matrix decompositions in linear algebra.

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Explores three ways to form quotient spaces using group actions and equivalence relations.

Covers the construction of an iterative method for linear systems, emphasizing matrix decomposition and convexity.

Explores the construction of solutions by Dirichlet-Laplace in general domains.