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AndroidFish
  • Member for 6 years, 8 months
  • Last seen more than 4 years ago
7 votes
3 answers
103 views

Prove $\Pi_{k=1}^\infty(1+q^k)=\Pi_{k=1}^\infty\frac{1}{(1-q^{(2k-1)})}$ are equivalent generating series.

5 votes
3 answers
102 views

Prove that $\lim_{n \to\infty} \int_0^1 \frac{x^n}{\sqrt{1+x^n}}\, \mathrm dx=0$.

4 votes
1 answer
88 views

Find two bounded sequences, $\{s_n\}_{n \in \mathbb N}$ and $\{t_n\}_{n \in \mathbb N}$, such that $\limsup(s_n+t_n))<\limsup(s_n)+\limsup(t_n)$

3 votes
1 answer
986 views

What is the probability that the sequence of $n$ integers between $1$ and $n$ contains exactly $n-2$ different integers?

3 votes
2 answers
687 views

Give an example where $UT$ is one-to-one, but $T$ isn't. Give an example where $UT$ is onto, but $T$ isn't.

3 votes
2 answers
782 views

Suppose G is a finite group. Let N be a normal subgroup of G and A an arbitrary subgroup. Verify that $|AN|=\frac{|A|*|N|}{|A \cap N|}$

2 votes
3 answers
300 views

If $\lvert f(x)-f(y) \rvert \le \lvert x-y \rvert ^2$ for all $x$ and $y$ in $\mathbb{R}$ then $f$ is a constant function [duplicate]

2 votes
3 answers
1k views

Number of ways to choose bagels

1 vote
2 answers
912 views

Prove that if $T:V\rightarrow V$ is additive (that is, $T(x+y)=T(x)+T(y)$ for all $x,y \in V$), then $T$ is linear.

1 vote
1 answer
25 views

Fix point interval tends to the fix point

1 vote
1 answer
30 views

Prove for two groups, one less than the other, the smaller is a cyclic subgroup of larger.

1 vote
1 answer
29 views

Find noninvertible $T:P(\mathbb R) \rightarrow P(\mathbb R)$ and $S:P(\mathbb R) \rightarrow P(\mathbb R)$ such that $TS=I_{P(\mathbb R)}$

1 vote
2 answers
54 views

What is $\bigcap_{n=1}^{\infty}[\frac{1}{3n}, 1+\frac{1}{n})$

1 vote
3 answers
56 views

The matrix $e^A$ is defined by $e^A=\Sigma_{k=0}^{\infty}\frac {A^k}{k!}$ Suppose M=$\begin{bmatrix}1 & 1\\0 & 1\end{bmatrix}$. Calculate $e^M$

1 vote
1 answer
52 views

Prove that if $\{v_1,v_2,\dots,v_n\}$ is orthonormal, then for any $v$, $\lVert v\rVert^2 \ge \Sigma_{j=1}^n \lvert \langle v,v_j \rangle \rvert$

1 vote
1 answer
2k views

Assume that $f$ is continuous at $0$ and $g$ is discontinuous at $0$. Prove that if $f(0) \neq 0$, then $f*g$ is not continuous at $0$

1 vote
1 answer
72 views

lucas numbers Prove that $l_0^2+l_1^2+...+l_n^2=l_n*l_n+1+2$ for $n \ge 0$

1 vote
2 answers
293 views

Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$

1 vote
1 answer
27 views

Let $V,W$ be complex inner product spaces. Fix $v \in V$ and $w \in W$ and define $T(u)=\langle u,v\rangle_V *w$. Find $T^*:W \rightarrow V$

1 vote
1 answer
277 views

Find isomorphism between $S_4/H$ and $S_3$ where $H={e,(12)(34),(13)(24),(14)(23)}$ using isomorphism theorem

1 vote
1 answer
49 views

Elementary Divisor Form Uncertainty

1 vote
0 answers
459 views

A finite abelian group $G$ has invariant factors $(m_1, m_2, ..., m_k)$. Show that $G$ has an element of order $s$ if and only if $s$ divides $m_k$.

1 vote
1 answer
41 views

Suppose $g,h,a∈G$ such that $h=aga^{−1}$. Prove that the formula $x↦ax$ defines a bijection of sets $Fix_X(g)→Fix_X(h)$

0 votes
1 answer
52 views

Determining the strength of information to vote for candidates.

0 votes
2 answers
78 views

Let $E \subseteq \mathbb{R}^n$ be compact. Let $D = sup\{d(x, y) : x, y ∈ E\}$. Prove that there exists $x_0, y_0$ in $E$ such that $d(x_0, y_0) = D$.

0 votes
0 answers
647 views

Prove that the rank of a nonzero $m \times n$ matrix $A$ is the largest number $r$ such that $A$ has an $r \times r$ minor with nonzero determinant.

0 votes
2 answers
285 views

Assume that $f:(0,∞)→ℝ$ is twice differentiable with $f(x)>0$ and $f'(x)<0$ for all $x \in (0, ∞)$. Prove that $f''(x)$ cannot always be negative.

0 votes
1 answer
140 views

Characteristic polynomial of unique matrix [duplicate]

0 votes
1 answer
64 views

Prove that $h:S \rightarrow \mathbb R^2$ defined by $h(s)=(f(s),g(s))$ is uniformly continuous on $S$.

0 votes
1 answer
252 views

Prove that a continuous function from $B(0,1) \subset \mathbb R^2$ to $\mathbb R$ can not be one-to-one.