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Marcos's user avatar
Marcos
  • Member for 1 year, 1 month
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5 votes
Accepted

If you have $2n$ people how many different ways can you pair them up?

4 votes

Cardinal of the set $A=\Big\{x=\frac pq\in\mathbb{Q} :|\sqrt 2-x|<\frac1{q^3}\Big\}$

4 votes
Accepted

Let $f \in Map(\mathbb{Z})$ be given by $f(n) = n+1$ for every $n \in \mathbb{Z}$. Find all elements in $Map(\mathbb{Z})$ that commute with $f$.

4 votes

Proving transitivity on relation: $aRb=7\mid |a-b|$

4 votes
Accepted

How to evaluate the sum $\sum_{n=1}^{\infty}{n^2}/{(n+1)!}$

3 votes
Accepted

Finding an an element with order equal to that of a coset

3 votes

Prove that $|Z(G)|=p$

3 votes

Not given a determinant, how can I prove an unknown is invertible?

3 votes
Accepted

Properties of radical of an ideal

2 votes
Accepted

Proving $\sqrt {P^ n}=P$ when $P$ is a prime ideal

2 votes
Accepted

How many functions $f:\{1,2,3,4,5\}\to\{1,2,3,4,5\}$ there are such that: $f^{-1}(\{1,2,3\})=\{2,3,4,5\}$and $f^{-1}(\{2,3,5\})=\{4,5\}$?

2 votes

The set of Fibonacci numbers formalized in set-theoretic notation: did I do it correctly?

2 votes

Proof of $aH=bH$ or $aH \cap bH=\emptyset$

2 votes

$\lim_{n \to \infty}{a^n \over n!} $.

2 votes
Accepted

If an invertible matrix $A$ satisfies $c||x|\leq ||Ax|| \leq C||x||$ for all $x$, can one say the same about its inverse?

2 votes

If $\cos\frac \pi{n+1}$ is a root of the equation $8x^3+4x^2-4x-1=0$, then find n $(n\in\mathbb N)$

1 vote
Accepted

How to show that $\sum_{i=1}^n\left(x_i^2 - \bar{x}^2\right) = \sum_{i=1}^n\left(x_i - \bar{x}\right)^2$

1 vote
Accepted

Can we show the product of two connected topological space is connected by a proof by contradiction?

1 vote
Accepted

$\int _a^bQ(x)\cdot w(x)dx=0$

1 vote

Solve $4(x+y+z+4) = xyz$

1 vote
Accepted

Trivial question about orthogonal complement

1 vote
Accepted

Calculate ${e^{At}}$ of $A = \left( {\begin{array}{*{20}{c}} i&j&k\\ i&j&k\\ i&j&k \end{array}} \right)$ knowing that $i+j+k=0 $

1 vote
Accepted

Hilbert-space operator norm in L2

1 vote
Accepted

Integral of $\frac{5z^2 - 8}{z^3-2z^2}$

1 vote
Accepted

Given equation has no integral solution.

1 vote

Connected and disconnected space

1 vote
Accepted

$\mathbb{Z}\rtimes\mathbb{Z}$ is left-orderable but not right-orderable.

1 vote

$\phi: \mathbb{R}[X] \to \mathbb{C}$ is a homomorphism such that: $\phi(X) = 1 + i$. What is $\ker \phi$?

1 vote

Necessary condition for a function to be odd

1 vote
Accepted

Simplifying $\frac{p^2q^2(1-\epsilon^2\cos^2t)}{p^2\cos^2t+q^2\sin^2t}$, where $\epsilon=\sqrt{1-(q/p)^2}$