User Wesley

27 votes

5 answers

4k views

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

functions notation

asked Jan 13, 2015 at 4:18

9 votes

4 answers

275 views

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

asked Jun 16, 2018 at 21:39

9 votes

7 answers

503 views

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

calculus integration limits convergence-divergence definite-integrals

asked Jul 3, 2018 at 0:51

8 votes

3 answers

295 views

$C_1$ and $C_2$ are non-crossing if they are translates of a convex disc

general-topology convex-analysis

asked May 4, 2019 at 17:01

7 votes

1 answer

1k views

Pigeonhole Principle Problem

pigeonhole-principle

asked Apr 29, 2019 at 19:08

7 votes

3 answers

12k views

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

linear-algebra linear-transformations

asked Feb 27, 2017 at 20:49

6 votes

3 answers

158 views

Five numbers whose difference is their gcd

elementary-number-theory

asked Feb 19, 2019 at 13:35

3 votes

1 answer

2k views

Showing that the Dirichlet function has no limit

real-analysis limits proof-verification

asked Nov 21, 2018 at 4:11

3 votes

1 answer

99 views

Infinitely many of $1,11,111,\dots$ is divisible by $2^{2019}+1$

number-theory

asked Apr 29, 2019 at 20:10

3 votes

1 answer

72 views

Decomposing a convex quadrilateral

discrete-geometry

asked May 5, 2019 at 10:21

3 votes

1 answer

119 views

Justification for cancelling variables in a rational expression

functions

asked Feb 18, 2015 at 21:38

3 votes

1 answer

150 views

Cancelling variable factors in a rational function

rational-functions

asked Apr 30, 2016 at 4:30

3 votes

2 answers

1k views

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

sequences-and-series

asked Jul 10, 2016 at 14:04

3 votes

5 answers

435 views

A complete residue system from an arithmetic progression

elementary-number-theory prime-numbers

asked Jul 21, 2016 at 21:53

2 votes

1 answer

121 views

Existence of basis of $P_2$ with no polynomial of degree 1

linear-algebra

asked Oct 7, 2016 at 22:38

2 votes

3 answers

64 views

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

recurrence-relations

asked Nov 9, 2016 at 1:37

2 votes

1 answer

2k views

What is the difference between a multivariate function and a vector-valued function?

functions vectors

asked Sep 30, 2015 at 0:21

2 votes

1 answer

4k views

Cases of reversible and irreversible operations in algebra

algebra-precalculus

asked Nov 16, 2015 at 2:56

2 votes

1 answer

2k views

Pulling a negative out of a square root

complex-numbers

asked Jan 19, 2016 at 0:28

2 votes

3 answers

81 views

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

real-analysis

asked Sep 27, 2017 at 1:24

2 votes

1 answer

562 views

Contrapositive of a quantified statement

logic first-order-logic quantifiers

asked Feb 3, 2018 at 6:06

2 votes

2 answers

2k views

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

combinatorics stirling-numbers

asked Mar 2, 2019 at 13:06

2 votes

3 answers

98 views

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

diophantine-equations

asked Mar 31, 2019 at 9:40

2 votes

3 answers

97 views

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

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

asked Mar 31, 2019 at 12:58

2 votes

1 answer

119 views

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

number-theory

asked Mar 31, 2019 at 15:28

2 votes

2 answers

175 views

Interpreting a problem in combinatorial geometry

combinatorics euclidean-geometry

asked Apr 1, 2019 at 13:15

2 votes

0 answers

503 views

Geometric mean of a sequence converges

real-analysis sequences-and-series proof-verification convergence-divergence

asked Oct 11, 2018 at 23:19

2 votes

1 answer

242 views

Group ring isomorphic to matrix ring

matrices ring-theory group-rings ring-isomorphism

asked Nov 28, 2018 at 15:46

2 votes

2 answers

353 views

Show that a ring of fractions and a quotient ring are isomorphic

abstract-algebra ring-theory

asked Dec 6, 2018 at 21:58

1 vote

0 answers

94 views

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

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

asked Dec 8, 2018 at 22:57

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78 Questions

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

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

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

$C_1$ and $C_2$ are non-crossing if they are translates of a convex disc

Pigeonhole Principle Problem

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

Five numbers whose difference is their gcd

Showing that the Dirichlet function has no limit

Infinitely many of $1,11,111,\dots$ is divisible by $2^{2019}+1$

Decomposing a convex quadrilateral

Justification for cancelling variables in a rational expression

Cancelling variable factors in a rational function

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

A complete residue system from an arithmetic progression

Existence of basis of $P_2$ with no polynomial of degree 1

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

What is the difference between a multivariate function and a vector-valued function?

Cases of reversible and irreversible operations in algebra

Pulling a negative out of a square root

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

Contrapositive of a quantified statement

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

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

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

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

Interpreting a problem in combinatorial geometry

Geometric mean of a sequence converges

Group ring isomorphic to matrix ring

Show that a ring of fractions and a quotient ring are isomorphic

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