User Wesley

13

20

votes

5

answers

2k

views

Why does notation for functions seem to be abused and ambiguous?

functions notation

Sep 23 at 10:15 Toby Bartels 679

2

8

votes

7

answers

230

views

Show that $\lim_{n \to \infty} \int_0^{\infty} \frac{1}{1+x^n}~dx = 1$

calculus integration limits convergence definite-integrals

Jul 3 at 15:54 Doug M 45.4k

4

8

votes

4

answers

197

views

Evaluate the integral $\int_0^{\infty}e^{-x} \sin x \log x ~ dx$

calculus integration definite-integrals

Jun 18 at 12:06 Shashi 7,377

2

6

votes

3

answers

118

views

Five numbers whose difference is their gcd

elementary-number-theory

Feb 20 at 6:41 FredH 3,685

1

3

votes

1

answer

42

views

Cancelling variable factors in a rational function

rational-functions

Aug 7 '16 at 15:13 Obinna Nwakwue 801

1

3

votes

5

answers

315

views

A statement about divisibility of relatively prime integers

elementary-number-theory prime-numbers

Jul 23 '16 at 5:47 Daniel Buck 2,818

3

votes

2

answers

436

views

Zero-based numbering vs. one-based numbering for sequences

sequences-and-series

Jul 10 '16 at 17:46 Community♦ 1

3

votes

1

answer

90

views

Justification for cancelling variables in a rational expression

functions

Feb 18 '15 at 23:31 GFauxPas 4,163

1

2

votes

3

answers

92

views

Does the equation $a^2+d^2+4=b^2+c^2$ have any solutions?

diophantine-equations

Apr 11 at 1:49 Sam 11

2

votes

2

answers

142

views

Interpreting a problem in combinatorial geometry

combinatorics euclidean-geometry

Apr 1 at 13:47 Servaes 30.9k

1

2

votes

1

answer

41

views

Infinite set of positive integers such that no subset sum is a square

number-theory

Mar 31 at 16:12 Μάρκος Καραμέρης 722

2

votes

3

answers

81

views

$f(n)+f(m) = q^2$ always has a solution

number-theory elementary-number-theory polynomials square-numbers

Mar 31 at 13:55 Dr. Mathva 3,588

2

votes

1

answer

38

views

Group ring isomorphic to matrix ring

matrices ring-theory group-rings ring-isomorphism

Nov 28 at 16:10 rschwieb 108k

1

2

votes

1

answer

148

views

Showing that the Dirichlet function has no limit

real-analysis limits proof-verification

Nov 21 at 5:02 астон вілла олоф мэллбэрг 40.7k

1

2

votes

0

answers

49

views

Geometric mean of a sequence converges

real-analysis sequences-and-series convergence

Oct 11 at 23:19 Wesley 619

2

votes

3

answers

55

views

Motivation for completing the rationals and proving that x^2=2 has a real solution

real-analysis

Sep 27 '17 at 2:10 Xander Henderson 15.2k

3

2

votes

3

answers

3k

views

Why does $\ker(T) = \{0\} \Leftrightarrow T$ is injective

linear-algebra linear-transformations

Feb 27 '17 at 21:54 user326159 1,448

1

2

votes

3

answers

61

views

How to prove a formula involving polynomial sequences and their recursive representation

recurrence-relations

Nov 9 '16 at 15:15 Brian M. Scott 461k

1

2

votes

1

answer

736

views

Pulling a negative out of a square root

complex-numbers

Jan 19 '16 at 1:22 Community♦ 1

1

vote

2

answers

39

views

Whether an area contains finitely many lattice points

geometry number-theory

Mar 28 at 1:31 Conrad 1,671

1

vote

2

answers

75

views

Computing $S(n,3)$, Stirling number of 2nd kind

combinatorics stirling-numbers

Mar 2 at 21:33 Mike Earnest 28.3k

1

vote

0

answers

55

views

Intersection of any 2 intervals $\implies$ all intervals intersect

proof-verification convex-geometry

Feb 24 at 16:29 Wesley 619

1

vote

1

answer

45

views

Showing an isomorphism between two quadratic rings

abstract-algebra ring-theory

Dec 9 at 2:18 Wesley 619

1

vote

0

answers

31

views

The cases in proving that a group of order 90 is not simple

abstract-algebra group-theory sylow-theory simple-groups

Dec 8 at 22:57 Wesley 619

1

vote

2

answers

70

views

Show that a ring of fractions and a quotient ring are isomorphic [duplicate]

abstract-algebra ring-theory

Dec 7 at 0:22 Bill Dubuque 214k

1

vote

0

answers

35

views

Show that $\sum_{n=1}^{\infty}\sin \left(\frac{n\pi}{3} \right)\frac{1}{n^r}$ diverges for $0<r<1$

sequences-and-series convergence divergent-series

Oct 8 at 20:05 Wesley 619

1

vote

1

answer

45

views

The normal subgroup of G generated by the set A

abstract-algebra group-theory normal-subgroups

Sep 19 at 3:20 Jonathan Dunay 1,405

1

vote

3

answers

117

views

Showing that the alternating group of degree n is normal

abstract-algebra permutation-cycles

Sep 12 at 6:09 matt stokes 580

1

vote

2

answers

270

views

Rewriting a statement in logical form

logic propositional-calculus logic-translation

Mar 28 '18 at 15:50 Bram28 64.8k

1

vote

1

answer

189

views

Contrapositive of a quantified statement

logic first-order-logic quantifiers

Feb 3 '18 at 10:29 Taroccoesbrocco 5,874

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70 Questions

Why does notation for functions seem to be abused and ambiguous?

Show that $\lim_{n \to \infty} \int_0^{\infty} \frac{1}{1+x^n}~dx = 1$

Evaluate the integral $\int_0^{\infty}e^{-x} \sin x \log x ~ dx$

Five numbers whose difference is their gcd

Cancelling variable factors in a rational function

A statement about divisibility of relatively prime integers

Zero-based numbering vs. one-based numbering for sequences

Justification for cancelling variables in a rational expression

Does the equation $a^2+d^2+4=b^2+c^2$ have any solutions?

Interpreting a problem in combinatorial geometry

Infinite set of positive integers such that no subset sum is a square

$f(n)+f(m) = q^2$ always has a solution

Group ring isomorphic to matrix ring

Showing that the Dirichlet function has no limit

Geometric mean of a sequence converges

Motivation for completing the rationals and proving that x^2=2 has a real solution

Why does $\ker(T) = \{0\} \Leftrightarrow T$ is injective

How to prove a formula involving polynomial sequences and their recursive representation

Pulling a negative out of a square root

Whether an area contains finitely many lattice points

Computing $S(n,3)$, Stirling number of 2nd kind

Intersection of any 2 intervals $\implies$ all intervals intersect

Showing an isomorphism between two quadratic rings

The cases in proving that a group of order 90 is not simple

Show that a ring of fractions and a quotient ring are isomorphic [duplicate]

Show that $\sum_{n=1}^{\infty}\sin \left(\frac{n\pi}{3} \right)\frac{1}{n^r}$ diverges for $0<r<1$

The normal subgroup of G generated by the set A

Showing that the alternating group of degree n is normal

Rewriting a statement in logical form

Contrapositive of a quantified statement