Question

$X_n$ s.t $E[\sup _n |X _{n+1}-X_n|]< \infty$ and $X_0 =0$. Prove that a.s $\limsup X _n=-\liminf X _n =\infty$ or $\lim X _n$ exsits and finite

score 44 · Answer 1 · 2026-04-17 02:15:53

44

Views

$X_n$ s.t $E[\sup _n |X _{n+1}-X_n|]< \infty$ and $X_0 =0$. Prove that a.s $\limsup X _n=-\liminf X _n =\infty$ or $\lim X _n$ exsits and finite

Published on 17 Apr 2026 - 2:15

score 91 · Answer 2 · 2026-04-14 21:57:33

91

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This Proof of Squeeze Theorem is simpler than textbook answer - is it incorrect?

Published on 14 Apr 2026 - 21:57

score 82 · Answer 3 · 2026-04-11 13:06:48

82

Views

Proof of Simpson's Paradox

Published on 11 Apr 2026 - 13:06

score 47 · Answer 4 · 2026-04-15 13:58:23

47

Views

$Gx$ is distributed uniformly in the set $\Bbb Z_2 ^n$.

Published on 15 Apr 2026 - 13:58

score 163 · Answer 5 · 2026-04-16 14:06:11

163

Views

Show that the possible ideals of a ring of quaternions over integers modulo an odd prime is either the $(0)$ or the set itself.

Published on 16 Apr 2026 - 14:06

score 61 · Answer 6 · 2026-04-17 06:13:54

61

Views

Prove Lipschitz continuity of exponent $\alpha$ implies uniform continuity

Published on 17 Apr 2026 - 6:13

score 135 · Answer 7 · 2026-05-05 22:55:37

135

Views

How do we calculate the integral $\int_{1}^{e}\frac{\ln(x + 1)}{2x + 2}\mathrm{d}x$?

Published on 05 May 2026 - 22:55

score 172 · Answer 8 · 2026-04-17 11:52:09

172

Views

Proof: Given two polynomials $f(x)$ and $g(x)$, there exist $Q(x)$ and $R(x)$ such that $f(x)=Q(x)g(x)+R(x)$ and $deg(R)<deg(g)$

Published on 17 Apr 2026 - 11:52

score 129 · Answer 9 · 2026-04-13 03:42:37

129

Views

Maths challenge question: Is my reasoning behind this question correct?

Published on 13 Apr 2026 - 3:42

score 76 · Answer 10 · 2026-04-12 16:59:03

76

Views

Is my proof that $\sqrt{p}$ is irrational ($p$ is a prime) valid?

Published on 12 Apr 2026 - 16:59

score 23 · Answer 11 · 2026-04-15 07:58:26

23

Views

Prove uniqueness of polynomials in polynomial division.

Published on 15 Apr 2026 - 7:58

score 47 · Answer 12 · 2026-04-17 04:29:43

47

Views

Prove that a family of functions is uniformly bounded

Published on 17 Apr 2026 - 4:29

score 54 · Answer 13 · 2026-04-15 21:51:41

If $a,b,c$ be in H.P., prove that $\dfrac{1}{a}+\dfrac{1}{b+c}, \dfrac{1}{b}+\dfrac{1}{c+a}, \dfrac{1}{c}+\dfrac{1}{a+b}$ are also in H.P.

score 44 · Answer 14 · 2026-04-12 03:20:15

44

Views

Question about powerset exercise in book of proof

Published on 12 Apr 2026 - 3:20

score 48 · Answer 15 · 2026-04-10 16:32:03

48

Views

For which values does a sequence have convergent subsequences?

Published on 10 Apr 2026 - 16:32

List Question

$X_n$ s.t $E[\sup _n |X _{n+1}-X_n|]< \infty$ and $X_0 =0$. Prove that a.s $\limsup X _n=-\liminf X _n =\infty$ or $\lim X _n$ exsits and finite

This Proof of Squeeze Theorem is simpler than textbook answer - is it incorrect?

Proof of Simpson's Paradox

$Gx$ is distributed uniformly in the set $\Bbb Z_2 ^n$.

Show that the possible ideals of a ring of quaternions over integers modulo an odd prime is either the $(0)$ or the set itself.

Prove Lipschitz continuity of exponent $\alpha$ implies uniform continuity

How do we calculate the integral $\int_{1}^{e}\frac{\ln(x + 1)}{2x + 2}\mathrm{d}x$?

Proof: Given two polynomials $f(x)$ and $g(x)$, there exist $Q(x)$ and $R(x)$ such that $f(x)=Q(x)g(x)+R(x)$ and $deg(R)<deg(g)$

Maths challenge question: Is my reasoning behind this question correct?

Is my proof that $\sqrt{p}$ is irrational ($p$ is a prime) valid?

Prove uniqueness of polynomials in polynomial division.

Prove that a family of functions is uniformly bounded

If $a,b,c$ be in H.P., prove that $\dfrac{1}{a}+\dfrac{1}{b+c}, \dfrac{1}{b}+\dfrac{1}{c+a}, \dfrac{1}{c}+\dfrac{1}{a+b}$ are also in H.P.

Question about powerset exercise in book of proof

For which values does a sequence have convergent subsequences?

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