User Kasper - Mathematics Stack Exchange

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	2,313 reputation	bio	website		visits	member for	5 months
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8

24

votes

2

answers

835

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Proof by contradiction vs Prove the contrapositive

jan 31 at 1:27 amWhy 54.7k

10

23

votes

1

answer

493

views

About Euclid's Elements and modern video games

geometry euclidean-geometry education math-software

may 1 at 21:30 Kasper 2,313

9

22

votes

7

answers

1

kviews

Does mathematics require axioms?

elementary-set-theory logic soft-question axioms foundations

apr 25 at 6:25 Matt E 58k

1

12

votes

4

answers

149

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What is symmetric about the symmetric group? [duplicate]

abstract-algebra group-theory symmetric-groups

feb 28 at 14:00 Tobias Kildetoft 4,726

4

8

votes

8

answers

506

views

How do I prove that a function is well defined?

functions logic proof-writing

feb 26 at 0:02 Asaf Karagila 91k

8

votes

3

answers

73

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$(\Bbb R \to \Bbb R : x\mapsto x^2)\equiv(\Bbb R \to \Bbb{R}_{\geq 0} : x \mapsto x^2) \not\equiv (\Bbb C \to \Bbb C:x\mapsto x^2)$

functions logic definition

feb 24 at 22:34 GEdgar 19k

7

votes

3

answers

88

views

Let $G$ a finite group of odd order. Let $N \triangleleft G$ and $|N|=17$. Prove that $N \subset Z(G)$.

abstract-algebra group-theory

apr 17 at 20:03 Alexander Gruber♦ 15.2k

7

votes

3

answers

324

views

Does the $\sum_{n=1}^\infty \frac{1}{n\sqrt[n]{n}}$ converge?

homework real-analysis sequences-and-series

feb 11 at 17:23 André Nicolas 161k

1

6

votes

2

answers

114

views

Is this correct? $rH=Hr^{-1}$

abstract-algebra group-theory

mar 14 at 22:36 Andreas Caranti 15.3k

1

6

votes

1

answer

141

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Does $\sum_{n=3}^\infty \frac {1}{(\log n)^{\log(\log(n)}}$ converge?

real-analysis sequences-and-series

mar 5 at 20:24 Arjang 2,437

5

votes

1

answer

67

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Is this reasoning correct?

abstract-algebra group-theory

mar 24 at 23:17 André Nicolas 161k

5

votes

2

answers

73

views

Prove that there exist no element of order 18 in $S_9$

abstract-algebra group-theory finite-groups

mar 20 at 13:44 joriki 92.6k

1

5

votes

3

answers

102

views

Let $G$ a group. Let $x\in G$. Assume that for every $y\in G, xyx=y^3$. Prove that $x^2=e$ and $y^8=e$ for all $y\in G$.

homework abstract-algebra

feb 18 at 21:12 i.a.m 1,475

5

votes

3

answers

151

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$\sum a_n$ converges $\iff \sum (\sqrt{1+a_n}-1)$ converges

homework real-analysis sequences-and-series

feb 13 at 21:28 Mhenni Benghorbal 14k

1

5

votes

2

answers

94

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$\sum_{k=1}^{z-1}\binom{k-1}{n-2}=\binom{z-1}{n-1}$

probability-theory binomial-coefficients

jan 30 at 21:41 Adi Dani 5,952

1

5

votes

10

answers

493

views

How to define the $0^0$? [duplicate]

real-analysis

dec 17 at 15:30 MJD 20.9k

4

votes

2

answers

41

views

How many different 2-regular graphs are there with 5 vertices?

combinatorics graph-theory

may 15 at 20:55 Douglas S. Stones 11.2k

4

votes

2

answers

36

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A point is in the boundary of $E$ if and only if it belongs to the closure of both $E$ and its complement.

real-analysis metric-spaces

apr 3 at 16:01 Berci 20.7k

4

votes

5

answers

133

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Let $x,y$ in a group G with uneven order. Let $x^2=y^2$. Show that $x=y$.

abstract-algebra group-theory

mar 24 at 21:52 Community♦ 1

4

votes

3

answers

92

views

Is there a quick trick to write permutations of $S_n$ as products of transpositions?

abstract-algebra finite-groups permutations

mar 16 at 15:54 amWhy 54.7k

4

votes

1

answer

59

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Let $f(x)=e^{-1/x}$ for $x>0$ and $f(x)=0$ for $x\leq 0$. Prove that $f^{(n)}(0)=0$ for all $n\in \Bbb N$.

real-analysis taylor-expansion

mar 7 at 16:02 Morgan Sherman 811

2

4

votes

2

answers

101

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Uniform convergence for $\sum_{n=1}^\infty n^\alpha x^{2n} (1-x)^2$

homework real-analysis uniform-convergence

mar 6 at 0:28 Mhenni Benghorbal 14k

4

votes

2

answers

181

views

Does the series $\sum \frac{x^n}{1+x^n}$ converge uniformly on $x\in [0,1)$?

homework real-analysis

mar 5 at 14:44 rschwieb 20.9k

4

votes

3

answers

100

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Let $g(x)=e^{-1/x^2}$ for $x\not=0$ and $g(0)=0$. Show that $g^{(n)}(0)=0$ for all $n\in\Bbb N$.

real-analysis taylor-expansion

mar 5 at 11:03 AndreasT 1,264

1

4

votes

3

answers

66

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Let $H_1,H_2$ be two subgroups of $G$. Show that $ G=H_1 \cup H_2 \implies G=H_1 \lor G=H_2 $

homework abstract-algebra

feb 25 at 19:55 Kasper 2,313

1

4

votes

4

answers

131

views

Prove that every isometry on $\mathbb{R}^2$ is bijective

real-analysis geometry

feb 18 at 17:34 André Nicolas 161k

4

votes

1

answer

134

views

$f$ continous at $x_0$ $⇒\lim_{h→0}∫_{x_0}^{x_0+h}\frac{f(t)}{h}=f(x_0)$

real-analysis limit integration continuity

jan 17 at 19:32 Community♦ 1

4

votes

2

answers

55

views

Proof that $\forall x\in (0,\frac{1}{e}),(x^x >e^\frac{-1}{e})$

real-analysis

dec 14 at 18:53 Nameless 7,937

3

votes

3

answers

211

views

$\int_a^b f(t)g(t)dt=f(x)\int_a^b g(t)dt$

real-analysis integral

apr 9 at 20:10 robjohn♦ 59.6k

2

3

votes

2

answers

112

views

A sequel for Elementary Analysis by Ross?

real-analysis analysis reference-request multivariable-calculus

apr 5 at 12:28 Kasper 2,313

Kasper

115 Questions