User MathNerd

10 votes

3 answers

483 views

Prove that there is no function $f:\Bbb{R}\to\Bbb{R}$ with $f(0)>0$ such that $\forall x,y\in\Bbb{R}, f(x+y)\geq f(x)+y f(f(x))$

asked Sep 24, 2014 at 7:43

8 votes

2 answers

1k views

A question about limits at infinity

calculus limits

asked Mar 27, 2014 at 11:37

6 votes

2 answers

102 views

A problem on distributing 29 disks on $7\times 7$ grid

probability combinatorics

asked Nov 9, 2014 at 10:50

5 votes

2 answers

230 views

Find examples of continuous functions $f:[0,1]\to[0,1]$ that satisfy $\forall x\in[0,1], f(f(x))=f(x)$ other than $f(x)=x$

calculus real-analysis continuity functional-equations

asked Sep 28, 2014 at 9:57

5 votes

1 answer

3k views

If every subspace of a vector space V is invariant under a linear transformation T then T is a scalar transformation

linear-algebra vector-spaces

asked Jan 8, 2014 at 12:58

5 votes

3 answers

234 views

Showing that the sequence $x_n=\frac{1}{3}x_{n-1}(4+x_{n-1}^3)$ where $x_0=-0.5$ quadratically converges

calculus sequences-and-series numerical-methods

asked Jul 31, 2015 at 15:58

5 votes

2 answers

13k views

Number of Arithmetic Operations in Gaussian-elimination/Gauss-Jordan Hybrid Method for Solving Linear Systems

linear-algebra matrices numerical-methods numerical-linear-algebra gaussian-elimination

asked Aug 24, 2015 at 9:16

4 votes

3 answers

444 views

Minimum number of steps required to visit every corner of a rectangular grid

combinatorics algorithms combinations searching

asked Mar 29, 2016 at 13:58

4 votes

1 answer

4k views

Number of edges in the Hasse diagram for the $\subseteq$ relation on the set $\mathcal{P}\{1,2,...,n\}$

combinatorics discrete-mathematics graph-theory relations

asked Aug 10, 2015 at 6:16

4 votes

1 answer

2k views

Finding the PDF from the CDF where the CDF is not differentiable at some point

calculus probability derivatives random-variables

asked Dec 19, 2014 at 15:29

4 votes

2 answers

157 views

Building neighborhoods around arbitrary real numbers that will contain "minimal" number of elements from the sequence $a_n=n\sin \frac{\pi n}{4}$

real-analysis sequences-and-series elementary-set-theory

asked Jul 13, 2018 at 19:40

4 votes

1 answer

312 views

Let $f,g:[0,1]\to\Bbb{R}$ such that $f(1)<0<f(0)$, $g$ is continuous on $[0,1]$ and $f+g$ is nondecreasing, Prove that $\exists x_0\in [0,1],f(x_0)=0$

calculus real-analysis continuity

asked Sep 27, 2014 at 17:42

4 votes

6 answers

727 views

Show that $\forall n\in\Bbb{N}, (3+\sqrt 7)^n+(3-\sqrt 7)^n\in\Bbb{Z}$ and that $\forall n\in\Bbb{N}, (2+\sqrt 2)^n+(2-\sqrt 2)^n\in\Bbb{Z}$

elementary-number-theory

asked Sep 21, 2014 at 18:13

3 votes

3 answers

197 views

Evaluating the limits $\lim_{(x,y)\to(\infty,\infty)}\frac{2x-y}{x^2-xy+y^2}$ and $\lim_{(x,y)\to(\infty,8)}(1+\frac{1}{3x})^\frac{x^2}{x+y}$

calculus limits multivariable-calculus

asked Aug 20, 2014 at 10:12

3 votes

4 answers

99 views

Showing that $3x^2+2x\sin(x) + x^2\cos(x) > 0$ for all $x\neq 0$

calculus

asked May 28, 2014 at 12:05

3 votes

6 answers

109 views

For any integer $n\geq 1$, define $\sin_n=\sin\circ ... \circ \sin$ ($n$ times). Prove that $\lim_{x\to 0}\frac{\sin_nx}{x}=1$ for all $n\geq 1$

calculus real-analysis limits

asked Sep 25, 2014 at 8:41

3 votes

3 answers

113 views

If $f$ satisfies $\forall x\in\Bbb{R},0\leq f'(x), f''(x)$ and if $\exists a\in\Bbb{R}$ such that $0<f'(a)$, Then $lim_{x\to\infty}f(x)=\infty$

calculus real-analysis limits derivatives

asked Sep 16, 2014 at 14:56

3 votes

1 answer

79 views

Construct a function $f:\Bbb{R}\to [0,\infty)$ such that every point $x\in\Bbb{Q}$ is a local strict minimum point of $f$

calculus real-analysis elementary-number-theory

asked Sep 23, 2014 at 16:40

3 votes

3 answers

1k views

Uniform continuity of $f(x)=(1-\cos(x))/\sin(x)$ on the interval $(0,1)$

calculus uniform-continuity

asked Apr 23, 2014 at 9:56

3 votes

0 answers

100 views

Book Suggestion for Approximating Integrals using Random Partitions

real-analysis integration probability-theory reference-request numerical-methods

asked May 4, 2018 at 16:53

3 votes

2 answers

2k views

Prove by Natural deduction that $\lnot\exists xP(x)\rightarrow\forall x\lnot P(x)$

logic first-order-logic predicate-logic natural-deduction formal-proofs

asked May 27, 2015 at 12:13

3 votes

1 answer

2k views

A Question about Shuffling a Deck of Cards

probability combinatorics

asked Oct 29, 2014 at 19:30

3 votes

1 answer

170 views

Calculating the x-intercept of the line that passes through the points $ (x_0,y_0)$ and $(x_1,y_1)$

numerical-methods

asked Jul 15, 2015 at 7:48

3 votes

2 answers

589 views

Calculating values of $1 - \cos(x)$ for $x$ near zero using computer arithmetic

trigonometry numerical-methods

asked Jul 22, 2015 at 16:18

3 votes

1 answer

435 views

Convergence of fixed-point iteration for $p$ times continuously differentiable function

calculus real-analysis sequences-and-series numerical-methods taylor-expansion

asked Jul 31, 2015 at 20:21

2 votes

2 answers

241 views

If $f$ is Lipschitz continuous on a closed interval $[a,b]$ such that $f([a,b])\subseteq [a,b]$ then it has a unique fixed-point

calculus real-analysis continuity fixed-point-theorems

asked Aug 1, 2015 at 13:36

2 votes

2 answers

408 views

A question about a fractal like iteratively defined function

calculus linear-algebra algorithms fractals chaos-theory

asked Sep 30, 2015 at 7:33

2 votes

1 answer

168 views

Determine under which conditions the formula $\phi[t/x]\leftrightarrow \forall x ((x=t)\rightarrow \phi)$ is logically true

logic first-order-logic

asked May 28, 2015 at 7:13

2 votes

0 answers

52 views

Proving some property of a set of logical expressions that satisfies some properties

logic compactness

asked Apr 11, 2015 at 17:35

2 votes

1 answer

2k views

Proving that a set with a ternary logical connective is functionally incomplete (i.e. inadequate)

logic propositional-calculus boolean-algebra

asked Apr 25, 2015 at 17:22

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125 Questions

Prove that there is no function $f:\Bbb{R}\to\Bbb{R}$ with $f(0)>0$ such that $\forall x,y\in\Bbb{R}, f(x+y)\geq f(x)+y f(f(x))$

A question about limits at infinity

A problem on distributing 29 disks on $7\times 7$ grid

Find examples of continuous functions $f:[0,1]\to[0,1]$ that satisfy $\forall x\in[0,1], f(f(x))=f(x)$ other than $f(x)=x$

If every subspace of a vector space V is invariant under a linear transformation T then T is a scalar transformation

Showing that the sequence $x_n=\frac{1}{3}x_{n-1}(4+x_{n-1}^3)$ where $x_0=-0.5$ quadratically converges

Number of Arithmetic Operations in Gaussian-elimination/Gauss-Jordan Hybrid Method for Solving Linear Systems

Minimum number of steps required to visit every corner of a rectangular grid

Number of edges in the Hasse diagram for the $\subseteq$ relation on the set $\mathcal{P}\{1,2,...,n\}$

Finding the PDF from the CDF where the CDF is not differentiable at some point

Building neighborhoods around arbitrary real numbers that will contain "minimal" number of elements from the sequence $a_n=n\sin \frac{\pi n}{4}$

Let $f,g:[0,1]\to\Bbb{R}$ such that $f(1)<0<f(0)$, $g$ is continuous on $[0,1]$ and $f+g$ is nondecreasing, Prove that $\exists x_0\in [0,1],f(x_0)=0$

Show that $\forall n\in\Bbb{N}, (3+\sqrt 7)^n+(3-\sqrt 7)^n\in\Bbb{Z}$ and that $\forall n\in\Bbb{N}, (2+\sqrt 2)^n+(2-\sqrt 2)^n\in\Bbb{Z}$

Evaluating the limits $\lim_{(x,y)\to(\infty,\infty)}\frac{2x-y}{x^2-xy+y^2}$ and $\lim_{(x,y)\to(\infty,8)}(1+\frac{1}{3x})^\frac{x^2}{x+y}$

Showing that $3x^2+2x\sin(x) + x^2\cos(x) > 0$ for all $x\neq 0$

For any integer $n\geq 1$, define $\sin_n=\sin\circ ... \circ \sin$ ($n$ times). Prove that $\lim_{x\to 0}\frac{\sin_nx}{x}=1$ for all $n\geq 1$

If $f$ satisfies $\forall x\in\Bbb{R},0\leq f'(x), f''(x)$ and if $\exists a\in\Bbb{R}$ such that $0<f'(a)$, Then $lim_{x\to\infty}f(x)=\infty$

Construct a function $f:\Bbb{R}\to [0,\infty)$ such that every point $x\in\Bbb{Q}$ is a local strict minimum point of $f$

Uniform continuity of $f(x)=(1-\cos(x))/\sin(x)$ on the interval $(0,1)$

Book Suggestion for Approximating Integrals using Random Partitions

Prove by Natural deduction that $\lnot\exists xP(x)\rightarrow\forall x\lnot P(x)$

A Question about Shuffling a Deck of Cards

Calculating the x-intercept of the line that passes through the points $ (x_0,y_0)$ and $(x_1,y_1)$

Calculating values of $1 - \cos(x)$ for $x$ near zero using computer arithmetic

Convergence of fixed-point iteration for $p$ times continuously differentiable function

If $f$ is Lipschitz continuous on a closed interval $[a,b]$ such that $f([a,b])\subseteq [a,b]$ then it has a unique fixed-point

A question about a fractal like iteratively defined function

Determine under which conditions the formula $\phi[t/x]\leftrightarrow \forall x ((x=t)\rightarrow \phi)$ is logically true

Proving some property of a set of logical expressions that satisfies some properties

Proving that a set with a ternary logical connective is functionally incomplete (i.e. inadequate)