User cardinal - Mathematics Stack Exchange

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	4,412 reputation	bio	website	none	visits	member for	2 years, 3 months
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41

60

votes

6

answers

3

kviews

Prove elementarily that $\sqrt[n+1] {(n+1)!} - \sqrt[n] {n!}$ is strictly decreasing

sequences-and-series

apr 3 at 3:36 Mark Hurd 372

22

36

votes

7

answers

783

views

Problems regarding $\{x_n \}$ defined by $x_1=1$; $x_n$ is the smallest distinct natural number such that $x_1+…+x_n$ is divisible by $n$.

mar 14 at 8:34 Marc van Leeuwen 23.7k

23

33

votes

4

answers

3

kviews

Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?

linear-algebra

sep 26 '11 at 20:12 Leon Lampret 2,625

32

31

votes

5

answers

3

kviews

Completion of rational numbers via Cauchy sequences

real-analysis reference-request

jun 13 '11 at 3:53 Community♦ 1

14

31

votes

5

answers

884

views

How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?

sequences-and-series trigonometry pi

may 7 at 15:34 robjohn♦ 59.2k

4

29

votes

6

answers

836

views

A sub-additivity inequality

real-analysis inequality

apr 28 '12 at 3:14 Community♦ 1

20

24

votes

3

answers

400

views

Square matrices satisfying certain relations must have dimension divisible by $3$

linear-algebra matrices contest-math

feb 26 at 10:26 YACP 8,985

11

20

votes

2

answers

972

views

I'm not sure about this inequality (how to prove or disprove it?)

inequality information-theory entropy

dec 21 at 6:35 Eric♦ 33.2k

6

16

votes

2

answers

1

kviews

The union of a strictly increasing sequence of $\sigma$-algebras is not a $\sigma$-algebra

homework measure-theory

may 25 '12 at 15:14 Jonas Teuwen 6,856

4

14

votes

1

answer

115

views

How low can the approval rating of a majority candidate be?

linear-programming voting-theory

aug 12 at 22:24 joriki 92.2k

7

13

votes

3

answers

412

views

Proving that $\sum_{i=0}^{n}\binom{n}{i}i^{n-i}(n-i)^{i}\le\frac{1}{2}n^n$

inequality binomial-coefficients summation

apr 6 at 1:22 i707107 1,099

11

12

votes

3

answers

1

kviews

Math Major: How to read textbooks in better style or method ? And how to select best books?

soft-question reference-request self-learning learning

apr 26 '11 at 22:13 Yuval Filmus 25.9k

5

11

votes

6

answers

1

kviews

Why are generating functions useful?

combinatorics generating-functions

jun 9 '12 at 13:47 Dylan Moreland 13.4k

6

11

votes

1

answer

146

views

If $\lambda_n \sim \mu_n$, is it true that $\sum \exp(-\lambda_n x) \sim \sum \exp(-\mu_n x)$ as $x \to 0$?

real-analysis sequences-and-series analysis asymptotics

jan 13 at 23:11 Community♦ 1

5

11

votes

1

answer

313

views

How do you prove Gautschi's inequality for the gamma function?

inequality special-functions gamma-function

jan 27 '12 at 19:05 robjohn♦ 59.2k

4

10

votes

3

answers

799

views

Axiom of Choice: Can someone explain the fallacy in this reasoning?

set-theory axiom-of-choice

apr 26 '11 at 13:40 Arturo Magidin 158k

4

9

votes

1

answer

853

views

What is the Kolmogorov Extension Theorem good for?

probability measure-theory stochastic-processes

apr 12 '12 at 11:08 Alexander Sokol 311

1

9

votes

2

answers

187

views

Convex Combinations of Low Probability Bernoulli Variables

probability random-variables

dec 27 at 11:11 saz 5,407

4

9

votes

2

answers

178

views

On the convexity of element-wise norm 1 of the inverse

convex-analysis norm convex-optimization inverse

apr 25 at 19:26 vqv 121

2

9

votes

2

answers

104

views

cosh x inequality

inequality convex-analysis

mar 15 at 18:37 Byron Schmuland 15.4k

5

8

votes

2

answers

305

views

A difficult symmetric inequality

inequality

dec 27 at 8:48 ivan 878

2

8

votes

2

answers

181

views

Probability of two points being split into different partitions.

probability stochastic-processes

may 6 at 10:27 mercio 11.2k

6

7

votes

2

answers

201

views

An inequality from the handbook of mathematical functions (by Abramowitz and Stegun)

calculus real-analysis inequality special-functions integral-inequality

dec 24 at 9:21 UnkleRhaukus 601

1

6

votes

1

answer

264

views

the limit of the ratio of two $\Gamma(x)$ functions

special-functions asymptotics gamma-function

oct 11 '11 at 2:50 Mike Spivey 25.8k

1

6

votes

2

answers

177

views

Show that the product converge

real-analysis infinite-product

feb 5 at 3:30 L. F. 3,601

3

5

votes

2

answers

142

views

Showing that a function is the sine function

analysis fourier-analysis

feb 13 '12 at 7:59 Eric♦ 33.2k

4

5

votes

0

answers

317

views

Idempotence and the Rao–Blackwell theorem

statistics probability-theory

apr 13 '12 at 1:58 cardinal 4,412

2

5

votes

1

answer

113

views

The ratio of two $L^p$ norms

measure-theory functional-analysis

may 6 '12 at 22:34 Julián Aguirre 14.6k

2

4

votes

1

answer

107

views

Find the distribution of $\log\left( \frac{\min(U_1,U_2,\ldots, U_n)^n}{U_1 U_2 \cdots U_n} \right)$ for iid $U_k \sim U(0,1)$

probability-distributions

may 22 '12 at 20:41 Sasha 41.4k

1

4

votes

0

answers

214

views

median of the F-distribution

statistics probability-distributions special-functions median

sep 25 at 21:15 fra 21

cardinal

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