Question

How to formalize notion of "up to ordering"

score 30 · Answer 1 · 2026-04-11 15:10:34

30

Views

How to formalize notion of "up to ordering"

Published on 11 Apr 2026 - 15:10

score 55 · Answer 2 · 2021-10-10 00:39:23

55

Views

why the number of Equivalence relations on a set is exactly the same as the number of distinct partitions of the set?

Published on 10 Oct 2021 - 0:39

score 23 · Answer 3 · 2021-10-11 15:13:00

23

Views

Equivalence relation defined on multi-indices (equality patterns).

Published on 11 Oct 2021 - 15:13

score 167 · Answer 4 · 2021-10-11 18:50:49

167

Views

When any set in $\mathbb{R}$ can be decomposed into disjoint sets, are all these sets always open sets/intervals?

Published on 11 Oct 2021 - 18:50

score 287 · Answer 5 · 2026-04-11 12:56:06

287

Views

Show that the equivalence classes of $R$ correspond to the elements of $\mathbb{Z}_{pq}$.

Published on 11 Apr 2026 - 12:56

score 44 · Answer 6 · 2021-10-13 20:32:13

44

Views

Show that the equivalence class $[0] = \mathbb Q$. What is $\left[\frac 13\right]$?

Published on 13 Oct 2021 - 20:32

score 49 · Answer 7 · 2021-10-13 21:13:51

49

Views

Let $\sim$ be a relation on $\mathbb R$ by $x \sim y \iff x-y \in\mathbb Q$. Show that $\sqrt{3} \notin \left[\sqrt{2}\right]$.

Published on 13 Oct 2021 - 21:13

score 65 · Answer 8 · 2021-10-13 22:08:12

65

Views

Is $x - y \leq 0$ an equivalence relation on $\mathbb{Z}$?

Published on 13 Oct 2021 - 22:08

score 113 · Answer 9 · 2021-10-14 20:22:58

113

Views

Show that $\sim$ is an equivalence relation.

Published on 14 Oct 2021 - 20:22

score 92 · Answer 10 · 2026-04-01 06:29:52

92

Views

How to show that for all $α, β \in Eq(X): α \circ β \subseteq α \vee β$?

Published on 01 Apr 2026 - 6:29

score 131 · Answer 11 · 2026-04-01 06:33:44

131

Views

What is the supremum and infimum of equivalence relations?

Published on 01 Apr 2026 - 6:33

score 61 · Answer 12 · 2021-10-17 15:54:29

Define the equivalence relation $R$ on $\mathbb{Z}$ associated with the function $f(x) = x^2 - 2x$. Write equivalence classes and quotient set.

score 54 · Answer 13 · 2026-04-11 21:28:42

54

Views

Equivalence class property

Published on 11 Apr 2026 - 21:28

score 22 · Answer 14 · 2026-04-12 07:05:50

22

Views

Big Union equivalence class

Published on 12 Apr 2026 - 7:05

score 87 · Answer 15 · 2026-04-01 06:32:16

87

Views

How do I prove that $\theta_1 \cup (\theta_1 \circ \theta_2) \cup (\theta_1 \circ \theta_2 \circ \theta_1) \: \cup ...$ is an equivalence relation?

Published on 01 Apr 2026 - 6:32

List Question

How to formalize notion of "up to ordering"

why the number of Equivalence relations on a set is exactly the same as the number of distinct partitions of the set?

Equivalence relation defined on multi-indices (equality patterns).

When any set in $\mathbb{R}$ can be decomposed into disjoint sets, are all these sets always open sets/intervals?

Show that the equivalence classes of $R$ correspond to the elements of $\mathbb{Z}_{pq}$.

Show that the equivalence class $[0] = \mathbb Q$. What is $\left[\frac 13\right]$?

Let $\sim$ be a relation on $\mathbb R$ by $x \sim y \iff x-y \in\mathbb Q$. Show that $\sqrt{3} \notin \left[\sqrt{2}\right]$.

Is $x - y \leq 0$ an equivalence relation on $\mathbb{Z}$?

Show that $\sim$ is an equivalence relation.

How to show that for all $α, β \in Eq(X): α \circ β \subseteq α \vee β$?

What is the supremum and infimum of equivalence relations?

Define the equivalence relation $R$ on $\mathbb{Z}$ associated with the function $f(x) = x^2 - 2x$. Write equivalence classes and quotient set.

Equivalence class property

Big Union equivalence class

How do I prove that $\theta_1 \cup (\theta_1 \circ \theta_2) \cup (\theta_1 \circ \theta_2 \circ \theta_1) \: \cup ...$ is an equivalence relation?

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