Question

Prove that $|(a,b)\cup (c,d)|=(b-a)+(d-c)\text{ if and only if }(a,b)\cap (c,d)=\emptyset.$ ("Measure, Integration & Real Analysis" by Sheldon Axler)

score 305 · Answer 1 · 2026-04-17 09:47:41

305

Views

Prove that $|(a,b)\cup (c,d)|=(b-a)+(d-c)\text{ if and only if }(a,b)\cap (c,d)=\emptyset.$ ("Measure, Integration & Real Analysis" by Sheldon Axler)

Published on 17 Apr 2026 - 9:47

score 56 · Answer 2 · 2026-04-14 12:49:54

56

Views

$\{2\}$ is both open and closed in $\{1,2,3\}$, equipped with the Euclidean metric

Published on 14 Apr 2026 - 12:49

score 48 · Answer 3 · 2026-04-16 23:26:23

48

Views

$f:[a, b] \rightarrow \mathbb{R}$ continous and $f(x) > 0$ for all $x$, then there exist $L > 0$ such that $f(x) \geq L$ for all $x$

Published on 16 Apr 2026 - 23:26

score 82 · Answer 4 · 2026-04-15 19:25:58

82

Views

Show that $F=\{f\in C([0,1]):f(s)\ge 0,\; \forall s\in[0,1]\}$ is closed in $\left(C([0,1]), d_{\infty}\right)$

Published on 15 Apr 2026 - 19:25

score 359 · Answer 5 · 2026-04-11 02:04:55

359

Views

Proof that a connected open set in $\mathbb{R}$ is path-connected

Published on 11 Apr 2026 - 2:04

score 135 · Answer 6 · 2026-04-17 08:21:10

135

Views

Solving $4^{x+\sqrt{x^2-2}}-5\cdot 2^{\sqrt{x^2-2}-1}=6$ for real $x$

Published on 17 Apr 2026 - 8:21

score 107 · Answer 7 · 2026-03-25 09:50:47

107

Views

Exercise 11, Section 7.2 of Hoffman’s Linear Algebra

Published on 25 Mar 2026 - 9:50

score 37 · Answer 8 · 2026-04-15 16:54:20

37

Views

Sequence of indicator functions have $L^2$-convergent subsequence.

Published on 15 Apr 2026 - 16:54

score 3.6k · Answer 9 · 2026-04-14 11:44:52

3.6k

Views

Don't Understand Mechanism behind Proof by Contradiction

Published on 14 Apr 2026 - 11:44

score 57 · Answer 10 · 2026-04-14 13:37:55

57

Views

Basic arithmetic question on the actuarial probability exam

Published on 14 Apr 2026 - 13:37

score 69 · Answer 11 · 2026-04-15 16:31:54

69

Views

Triple integral - ellipsoid - check answer

Published on 15 Apr 2026 - 16:31

score 47 · Answer 12 · 2026-04-12 15:26:46

47

Views

Computation of Statistical Curvature for a Distribution

Published on 12 Apr 2026 - 15:26

score 101 · Answer 13 · 2026-04-12 14:48:11

101

Views

Minimizing a function in $\mathbb R^3.$

Published on 12 Apr 2026 - 14:48

score 82 · Answer 14 · 2026-04-17 09:05:11

82

Views

Solving system of three equations

Published on 17 Apr 2026 - 9:05

score 64 · Answer 15 · 2026-04-10 23:52:35

64

Views

Proof by contradiction that an open interval in $\mathbb{R}$ is path-connected if it is connected

Published on 10 Apr 2026 - 23:52

List Question

Prove that $|(a,b)\cup (c,d)|=(b-a)+(d-c)\text{ if and only if }(a,b)\cap (c,d)=\emptyset.$ ("Measure, Integration & Real Analysis" by Sheldon Axler)

$\{2\}$ is both open and closed in $\{1,2,3\}$, equipped with the Euclidean metric

$f:[a, b] \rightarrow \mathbb{R}$ continous and $f(x) > 0$ for all $x$, then there exist $L > 0$ such that $f(x) \geq L$ for all $x$

Show that $F=\{f\in C([0,1]):f(s)\ge 0,\; \forall s\in[0,1]\}$ is closed in $\left(C([0,1]), d_{\infty}\right)$

Proof that a connected open set in $\mathbb{R}$ is path-connected

Solving $4^{x+\sqrt{x^2-2}}-5\cdot 2^{\sqrt{x^2-2}-1}=6$ for real $x$

Exercise 11, Section 7.2 of Hoffman’s Linear Algebra

Sequence of indicator functions have $L^2$-convergent subsequence.

Don't Understand Mechanism behind Proof by Contradiction

Basic arithmetic question on the actuarial probability exam

Triple integral - ellipsoid - check answer

Computation of Statistical Curvature for a Distribution

Minimizing a function in $\mathbb R^3.$

Solving system of three equations

Proof by contradiction that an open interval in $\mathbb{R}$ is path-connected if it is connected

Trending Questions

Popular # Hahtags

Popular Questions