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Top Questions

7 votes
3 answers
442 views

$( \ X\to G \ , \ \star \ )$ is a group if $(\varphi \star \psi)(a) = \varphi(a) \star \psi(a)$

11 votes
1 answer
471 views

Intuitive Explanation for Number of Dyck Paths Never Going Above Diagonal of a Rectangle

6 votes
2 answers
408 views

How many points does a line intersect a sphere in an infinite-dimensional normed vector space?

5 votes
4 answers
243 views

Simpler proof that $y^3[d^2y/dx^2]$ is a constant if $y^2=ax^2+bx+c$?

3 votes
2 answers
236 views

Longest geometric progression of primes

11 votes
3 answers
133 views

Prove $\sum_{i,j:i<j} μ(E_{i} \cap E_{j} )=\infty$.

10 votes
3 answers
202 views

Is there a purely topological proof that a certain topological space derived from logical compactness is compact?

4 votes
3 answers
679 views

If someone wins 3000 rounds of a game out of 100000 numbered rounds of a game, what is the expected no. of last-3-digits of a round that they solved?

8 votes
1 answer
389 views

What is an instanton? (On a complex surface or a differentiable 4-manifold )

5 votes
2 answers
235 views

Why aren't $\int_0^\pi\int_{-1}^1e^rdr\,d\theta$ and $\int_0^{2\pi}\int_0^1e^rdr\,d\theta$ equal? Doesn't this violate the Change of Variables thm?

8 votes
4 answers
231 views

How to evaluate $\int^{\infty}_0 \frac{x^{1010}}{(1 + x)^{2022}} dx$?

7 votes
1 answer
351 views

Rank 1 operator on an infinite dimensional vector space number of eigenvalues.

4 votes
5 answers
190 views

How do I integrate $\dfrac{\sin(x)}{e^x+1}$?

6 votes
1 answer
389 views

Why an LTI system with some zero eigenvalues still stable?

7 votes
3 answers
182 views

How to evaluate the sum of $\sum_{n=0}^{\infty}\frac{1}{3n^{2}+4n+1}$

6 votes
1 answer
127 views

Is there a term for abelian groups in which you can divide by natural numbers?

4 votes
3 answers
123 views

For what values of $p>0$ is $\lim_{n\rightarrow\infty}\int_0^n\frac{(1-\frac{x}{n})^ne^x}{n^p}dx=0$?

6 votes
3 answers
256 views

Why does this cycle of 44 show up in the Collatz Conjecture?

2 votes
2 answers
145 views

Why $f^2(x) \ne f(x)^2$?

10 votes
1 answer
378 views

Can the real numbers be equally split into two sets of same measure?

2 votes
3 answers
105 views

$x=y\Rightarrow \arg x=\arg y$

0 votes
2 answers
214 views

How to prove that $19 < \gcd(5^{44}-1,1+22!)$? [duplicate]

6 votes
3 answers
121 views

Criteria for $3 \times 3$ matrix to positive definite

17 votes
2 answers
378 views

Collatz conjecture but with $n^2-1$ instead of $3n+1.$ Does the sequence starting with $13$ go to infinity?

6 votes
4 answers
173 views

Inequality involving sums with binomial coefficient

11 votes
1 answer
219 views

The coupon collector's most collected coupon

3 votes
3 answers
237 views

Can a manifold be reconstructed from its charts?

4 votes
2 answers
214 views

How to see that "two manifolds are diffeomorphic when you can give them each a coordinate atlas with the same transition maps"

2 votes
1 answer
122 views

What has Godel exactly shown about $\mathsf{CH}$?

3 votes
4 answers
120 views

Coin change problem with specific multiples

4 votes
4 answers
119 views

Eigenvectors & eigenvalues of "nearby" matrices [duplicate]

5 votes
3 answers
248 views

Prove that $\sum_{n=0}^\infty \frac{1}{(2n+1)^2}=\frac{\pi^2}{8}$

5 votes
2 answers
191 views

Derivative of the inverse of a symmetric matrix w.r.t itself

3 votes
3 answers
184 views

Existence Problem of pigeonhole, selecting among a set of 50 numbers.

4 votes
2 answers
134 views

Is a continuous function on compact convex set where the boundary is mapped to the set a self mapping?

2 votes
4 answers
77 views

What is the right adjoint to the functor $\sf{Psh}\to\sf{Set}$ which evaluates the presheaf on the whole space?

0 votes
1 answer
206 views

$ \sum_{i \in I} a_i = \sum_{j \in J} a_j $ for distinct $ I,J \subseteq \{1,\ldots,n\} $ if $ \sum_{i=1}^n a_i < 2^n - 1 $? [closed]

0 votes
3 answers
70 views

Is $ \{A\in \mathbb{R}^{n,n}: 0<\det(A)<2\} $ compact?

2 votes
2 answers
189 views

Solving $ A\frac{\partial z}{\partial x} + B \frac{\partial^2 z}{ \partial x \partial y} + C \frac{\partial^3 z}{\partial x \partial^2 y} = 0 $?

3 votes
5 answers
88 views

Is it possible to compute $-\log\left({\sqrt{1.8\times 10^{-5}\times 0.1}}\right)$ without a calculator?

4 votes
3 answers
140 views

Prove $\sum \frac{n^{p+1}}{a_1+2^pa_2+\cdots+n^pa_n}$ is convergent.

5 votes
2 answers
107 views

Show that $ \binom{n}{i\;j\;k} \le \binom{n}{m\;m\;m} $

1 vote
1 answer
219 views

Does the remainder theorem work for constant function?

4 votes
1 answer
271 views

Can mathematics distinguish left and right?

4 votes
1 answer
200 views

Multiplicative energy and Cauchy-Schwartz

2 votes
3 answers
92 views

$2ix^4 − 10x^3 + (4 − 2i)x + 8 + 6i$ irreducible in $\mathbb Z[i][x]$ and in $\mathbb Q[i][x]$

3 votes
4 answers
92 views

Prove that $\lim_{(x,y) \to (0,0)} \frac{xy(x-y)}{x^3 + y^3}$ does not exist

5 votes
2 answers
161 views

Durrett's Probability: Theorem 6.2.6


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