Question

Why do we use the term "equivalent" with Operators but "equal" with Functions?

score 367 · Answer 1 · 2014-07-30 19:43:21

367

Views

Why do we use the term "equivalent" with Operators but "equal" with Functions?

Published on 30 Jul 2014 - 19:43

score 29.7k · Answer 2 · 2026-03-29 03:35:57

29.7k

Views

If R is $(a,b)R(c,d) \iff a+d =b+c$ show that $R$ is an equivalence relation.

Published on 29 Mar 2026 - 3:35

score 880 · Answer 3 · 2014-08-02 01:13:29

880

Views

Solve for ? - undetermined inequality symbol

Published on 02 Aug 2014 - 1:13

score 109 · Answer 4 · 2026-03-25 09:26:35

109

Views

Expressing an formula in term of another one

Published on 25 Mar 2026 - 9:26

score 67 · Answer 5 · 2026-03-29 05:44:15

suppose $R$ is an equivalence relation on $A$ such that there are only finitely many distinct equivalence classes $A_1,A_2,\ldots,A_k$ w.r.t $R$

score 1.8k · Answer 6 · 2014-08-09 07:47:30

1.8k

Views

Is $R=\left \{ (a,a),(a,b),(b,a),(b,b),(c,c),(c,d),(d,c),(d,d) \right \}$ an equivalence relation on $X$?

Published on 09 Aug 2014 - 7:47

score 503 · Answer 7 · 2026-03-29 05:50:00

503

Views

Geometric/visual interpretation of transitivity for equivalence relations on $\mathbb{R}$

Published on 29 Mar 2026 - 5:50

score 466 · Answer 8 · 2026-03-29 05:44:13

466

Views

Let R be the relation on ℤ+→ℤ+ defined by (a,b)R(c,d) if and only if a-2d=c-2b. List all the elements of the equivalence class [(3,3)].

Published on 29 Mar 2026 - 5:44

score 50 · Answer 9 · 2014-08-25 17:20:47

50

Views

Comparing two circularly shifted matrices

Published on 25 Aug 2014 - 17:20

score 706 · Answer 10 · 2026-03-29 05:50:21

706

Views

Is the relation $a\mathrel R b \iff f(a) \equiv f(b)$ an equivalence relation?

Published on 29 Mar 2026 - 5:50

score 492 · Answer 11 · 2014-08-26 08:54:51

492

Views

How would I show that R is an equivalence relation?

Published on 26 Aug 2014 - 8:54

score 951 · Answer 12 · 2026-03-27 20:31:19

951

Views

Equivalence class for the relation of having the same set of prime divisors

Published on 27 Mar 2026 - 20:31

score 51 · Answer 13 · 2014-08-27 14:25:08

prove the following equivalence $\ln(-\frac{l-x+\sqrt{r^2+(l-x)}}{l+x-\sqrt{r^2+(l+x)}})={}$ArcSinh$(\frac{l+x}{r})+{}$ArcSinh$(\frac{l-x}{r})$

score 75 · Answer 14 · 2026-03-29 05:42:43

75

Views

What does it mean for a binary relation to be an order on "equivalence classes" under another binary relation

Published on 29 Mar 2026 - 5:42

score 1k · Answer 15 · 2026-03-29 05:42:52

1k

Views

Proving that a relation is an equivalence relation

Published on 29 Mar 2026 - 5:42

List Question

Why do we use the term "equivalent" with Operators but "equal" with Functions?

If R is $(a,b)R(c,d) \iff a+d =b+c$ show that $R$ is an equivalence relation.

Solve for ? - undetermined inequality symbol

Expressing an formula in term of another one

suppose $R$ is an equivalence relation on $A$ such that there are only finitely many distinct equivalence classes $A_1,A_2,\ldots,A_k$ w.r.t $R$

Is $R=\left \{ (a,a),(a,b),(b,a),(b,b),(c,c),(c,d),(d,c),(d,d) \right \}$ an equivalence relation on $X$?

Geometric/visual interpretation of transitivity for equivalence relations on $\mathbb{R}$

Let R be the relation on ℤ+→ℤ+ defined by (a,b)R(c,d) if and only if a-2d=c-2b. List all the elements of the equivalence class [(3,3)].

Comparing two circularly shifted matrices

Is the relation $a\mathrel R b \iff f(a) \equiv f(b)$ an equivalence relation?

How would I show that R is an equivalence relation?

Equivalence class for the relation of having the same set of prime divisors

prove the following equivalence $\ln(-\frac{l-x+\sqrt{r^2+(l-x)}}{l+x-\sqrt{r^2+(l+x)}})={}$ArcSinh$(\frac{l+x}{r})+{}$ArcSinh$(\frac{l-x}{r})$

What does it mean for a binary relation to be an order on "equivalence classes" under another binary relation

Proving that a relation is an equivalence relation

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