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MathNerd
  • Member for 8 years, 9 months
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10 votes
3 answers
483 views

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

8 votes
2 answers
1k views

A question about limits at infinity

6 votes
2 answers
102 views

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

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 $f(x)=x$

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

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

5 votes
2 answers
13k views

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

4 votes
3 answers
439 views

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

4 votes
1 answer
4k views

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

4 votes
1 answer
2k views

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

4 votes
2 answers
157 views

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

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 $\exists x_0\in [0,1],f(x_0)=0$

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 $\forall n\in\Bbb{N}, (2+\sqrt 2)^n+(2-\sqrt 2)^n\in\Bbb{Z}$

3 votes
3 answers
197 views

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

3 votes
4 answers
99 views

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

3 votes
6 answers
108 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 $n\geq 1$

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 $lim_{x\to\infty}f(x)=\infty$

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 $f$

3 votes
3 answers
1k views

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

3 votes
0 answers
100 views

Book Suggestion for Approximating Integrals using Random Partitions

3 votes
2 answers
2k views

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

3 votes
1 answer
2k views

A Question about Shuffling a Deck of Cards

3 votes
1 answer
170 views

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

3 votes
2 answers
582 views

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

3 votes
1 answer
434 views

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

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

2 votes
2 answers
408 views

A question about a fractal like iteratively defined function

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

2 votes
0 answers
52 views

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

2 votes
1 answer
2k views

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

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