Question

Have I correctly proved that $\lim_{||(x,y)||\to\infty}\frac1{y-x}\int_x^y\exp(-1/|t|)dt$ equals $1$?

score 288 · Answer 1 · 2026-04-16 09:32:30

288

Views

Have I correctly proved that $\lim_{||(x,y)||\to\infty}\frac1{y-x}\int_x^y\exp(-1/|t|)dt$ equals $1$?

Published on 16 Apr 2026 - 9:32

score 105 · Answer 2 · 2026-04-17 12:15:30

105

Views

Prove every infinite directed graph has infinite strict linear order or...

Published on 17 Apr 2026 - 12:15

score 118 · Answer 3 · 2026-04-16 12:18:34

118

Views

Is it a rigorous way to show that $x_n = 1 + {1^2\over 4} + {2^2\over 4^2} + \cdots + {n^2\over 4^n}$ is convergent?

Published on 16 Apr 2026 - 12:18

score 43 · Answer 4 · 2026-04-14 06:36:37

43

Views

Prove that if $a,b \ge2$ such that $a^b-1$ is prime, then $a=2$

Published on 14 Apr 2026 - 6:36

score 415 · Answer 5 · 2026-04-12 20:59:04

415

Views

Example of a proposition that is true when its quantifier ranges over integers, but false over rationals

Published on 12 Apr 2026 - 20:59

score 61 · Answer 6 · 2026-04-12 18:47:48

61

Views

proposition with quantifier 5

Published on 12 Apr 2026 - 18:47

score 83 · Answer 7 · 2026-04-16 09:31:25

83

Views

show that $a(1-b)$ and $b(1-a)$ can not both be greater than 1/4 for any two $a,b \in \mathbb{N}$

Published on 16 Apr 2026 - 9:31

score 220 · Answer 8 · 2026-04-14 03:33:43

220

Views

Orientation preserving homeomorphism on a torus

Published on 14 Apr 2026 - 3:33

score 637 · Answer 9 · 2026-04-15 05:30:52

637

Views

Iwahori versus Bruhat decompositions

Published on 15 Apr 2026 - 5:30

score 35 · Answer 10 · 2026-04-12 12:26:30

35

Views

Proof: Matrix has just non-negative real eigenvalues

Published on 12 Apr 2026 - 12:26

score 109 · Answer 11 · 2026-04-11 20:53:13

109

Views

Help with a bit more rigorous proof of the chain rule.

Published on 11 Apr 2026 - 20:53

score 157 · Answer 12 · 2026-04-17 18:40:40

157

Views

Proof verification of $\left(1+{1\over n}\right)^n > e^{1-1/n}$ for all $n\in\Bbb N$.

Published on 17 Apr 2026 - 18:40

score 112 · Answer 13 · 2026-04-13 05:03:22

112

Views

Exercise about finding an orthonormal basis

Published on 13 Apr 2026 - 5:03

score 57 · Answer 14 · 2026-04-16 01:05:50

57

Views

If $(a_n)\to\infty$, then $(1/a_n)\to0$

Published on 16 Apr 2026 - 1:05

score 648 · Answer 15 · 2026-04-15 05:15:31

648

Views

Find the long-term mean number of cars in line at the toll booth.

Published on 15 Apr 2026 - 5:15

List Question

Have I correctly proved that $\lim_{||(x,y)||\to\infty}\frac1{y-x}\int_x^y\exp(-1/|t|)dt$ equals $1$?

Prove every infinite directed graph has infinite strict linear order or...

Is it a rigorous way to show that $x_n = 1 + {1^2\over 4} + {2^2\over 4^2} + \cdots + {n^2\over 4^n}$ is convergent?

Prove that if $a,b \ge2$ such that $a^b-1$ is prime, then $a=2$

Example of a proposition that is true when its quantifier ranges over integers, but false over rationals

proposition with quantifier 5

show that $a(1-b)$ and $b(1-a)$ can not both be greater than 1/4 for any two $a,b \in \mathbb{N}$

Orientation preserving homeomorphism on a torus

Iwahori versus Bruhat decompositions

Proof: Matrix has just non-negative real eigenvalues

Help with a bit more rigorous proof of the chain rule.

Proof verification of $\left(1+{1\over n}\right)^n > e^{1-1/n}$ for all $n\in\Bbb N$.

Exercise about finding an orthonormal basis

If $(a_n)\to\infty$, then $(1/a_n)\to0$

Find the long-term mean number of cars in line at the toll booth.

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