List questions from equivalence-relations

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Equivalent definitions of congruences (in context of universal algebra)

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210

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What is a discrete congruence?

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Suppose that $e \sim f$ but $f \nsim g$ (i.e. $f$ is not homotopic to $g$). Is it possible that $g \sim e$?

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Showing that a relation is an equivalence relation

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Relation is transitive or not?

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Let the relation $\sim$ on $\mathbb{Q}$ be defined as follows: $x\sim y \Leftrightarrow x- \lfloor x \rfloor= y-\lfloor y \rfloor$

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If $R$ is symmetric and transitive then prove that $R$ is reflexive

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Find the canonical representative of the matrix equivalence class of the matrix $A$.

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What is the equivalent class of $\{a_1,...,a_n\}$

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573

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Does the empty set permit zero or one equivalence classes?

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235

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Equivalence closure

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Isomorphism between different definitions of Integers

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"Quotient" of category by arbitrary reflexive relation

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36

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Element choice for equivalence relation

Published on 11 Apr 2026 - 21:27

List Question

Is this equivalence relation correct?

Equivalent definitions of congruences (in context of universal algebra)

What is a discrete congruence?

Suppose that $e \sim f$ but $f \nsim g$ (i.e. $f$ is not homotopic to $g$). Is it possible that $g \sim e$?

Showing that a relation is an equivalence relation

Relation is transitive or not?

Let the relation $\sim$ on $\mathbb{Q}$ be defined as follows: $x\sim y \Leftrightarrow x- \lfloor x \rfloor= y-\lfloor y \rfloor$

If $R$ is symmetric and transitive then prove that $R$ is reflexive

Find the canonical representative of the matrix equivalence class of the matrix $A$.

What is the equivalent class of $\{a_1,...,a_n\}$

Does the empty set permit zero or one equivalence classes?

Equivalence closure

Isomorphism between different definitions of Integers

"Quotient" of category by arbitrary reflexive relation

Element choice for equivalence relation

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