List questions from equivalence-relations

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How are these integrals equal?

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Define a relation $R$ on $\mathbb{R}$ as follows: $(x,y) \in R \iff (x-y)(x^{2} + y^{2} - 1) = 0$.

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Matrix similarity is an equivalence relation

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Determining Equivalence class

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How many equivalence classes does a set have

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Relation of subsets of a quotient sets by the same relation

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Let $R \in A$ such that $|\mathbb{N}/R|=2$, Proof if $R$ has finite equivalence class so $[R]_E$ is countable

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Is this an equivalence relation? $xRy$ if and only if $|x+y| = |x| + |y|$

Published on 18 Aug 2017 - 20:54

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Determine an equivalence class of an element

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Commutative pairs of relations do not define an equivalence relation

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Is an anti-symmetric Relation always Transitive?

Published on 20 Aug 2017 - 16:18

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$S$ is the set of Integers, $a,b$ both belongs to $S$, $a\sim b$ if both $a>b$ and $b>a$.

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Understanding Equivalence Classes?

Published on 25 Aug 2017 - 20:46

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Is this possible to define the continuous map from equivalent class?

Published on 28 Aug 2017 - 9:01

List Question

Finding same equivalence classes for $(x,y) \in R \iff x-y \in \mathbb{Z}$

How are these integrals equal?

Define a relation $R$ on $\mathbb{R}$ as follows: $(x,y) \in R \iff (x-y)(x^{2} + y^{2} - 1) = 0$.

Matrix similarity is an equivalence relation

Determining Equivalence class

How many equivalence classes does a set have

Relation of subsets of a quotient sets by the same relation

Let $R \in A$ such that $|\mathbb{N}/R|=2$, Proof if $R$ has finite equivalence class so $[R]_E$ is countable

Is this an equivalence relation? $xRy$ if and only if $|x+y| = |x| + |y|$

Determine an equivalence class of an element

Commutative pairs of relations do not define an equivalence relation

Is an anti-symmetric Relation always Transitive?

$S$ is the set of Integers, $a,b$ both belongs to $S$, $a\sim b$ if both $a>b$ and $b>a$.

Understanding Equivalence Classes?

Is this possible to define the continuous map from equivalent class?

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