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csch2
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12 votes
2 answers
877 views

Asymptotic behavior of a sequence of integrals of non-analytic functions

6 votes
2 answers
2k views

Is using the "contains" symbol $\ni$ frowned upon?

5 votes
1 answer
136 views

Not every compact subset of $\mathbb{R}$ is the support of a continuous function

4 votes
1 answer
260 views

If $T_n\to T$ in the weak operator topology, does $p(T_n)\to p(T)$ in the weak operator topology for any polynomial $p$?

4 votes
1 answer
223 views

Proving $\frac{d}{dx}a^x=a^x\ln a$ from the integral definition of the natural logarithm

3 votes
3 answers
101 views

Prove that $\frac{x^{i+1}}{-2+2i}-\frac{x^{-i+1}}{2+2i}=\frac{x\sin(\ln(x))-x\cos(\ln(x))}{2}$

3 votes
2 answers
217 views

What is the cardinality of the set of convergent real-valued sequences?

2 votes
0 answers
40 views

Critical points of the Jacobi amplitude function

2 votes
3 answers
994 views

Show that the sequence defined by $x_{n+1}=x_n^2+\frac{1}{4}$ is convergent

2 votes
5 answers
273 views

$\varepsilon-\delta$ Proof: $\lim\limits_{x\to0}e^x=1$

2 votes
1 answer
505 views

Volume between cone and sphere of radius $\sqrt2$ with surface integral

2 votes
1 answer
256 views

Solutions of the differential equation $\dot{x}^2-2x=1$

2 votes
1 answer
859 views

General formula for volume integral of scalar field?

2 votes
0 answers
40 views

Question on Taylor's PDE, Volume 2, Problem 8.4.10

2 votes
3 answers
540 views

Does the ascending chain condition only apply to countable chains of ideals?

2 votes
1 answer
603 views

Construction of open set dense in $[0,1]$ with measure $\varepsilon$

2 votes
2 answers
77 views

Pointwise limit of $f_N(x)=\frac{1}{N(x^2+1)}\cdot\sum_{n=1}^N\cos(nx)$

2 votes
0 answers
39 views

Unital semiring of sets contains the empty set

1 vote
1 answer
173 views

Does locally uniform convergence preserve analyticity?

1 vote
1 answer
88 views

Why do we need invariance of domain to conclude that the neighborhood in the definition of a manifold is open?

1 vote
0 answers
54 views

Where to find examples of mean-bounded operators?

1 vote
0 answers
41 views

Fields non-trivially seen to be isomorphic to the real numbers by the uniqueness of a complete ordered field

1 vote
1 answer
176 views

Constructing a field from a direct product of fields

1 vote
1 answer
250 views

Generalizing Cauchy formula for repeated integration to convolutions

1 vote
1 answer
193 views

Proof verification: countable intersection of dense $G_\delta$'s in a complete metric space is dense

1 vote
1 answer
1k views

Proof verification: If $a\in A$ is an upper bound for $A$, then $a=\sup A$

1 vote
1 answer
65 views

Proof verification for linear subspaces from Michael Taylor's linear algebra notes

1 vote
2 answers
103 views

Is this a legitimate way to write the multivariable Taylor series formula?

1 vote
2 answers
1k views

Where is the solution $y=0$ when solving a linear homogeneous constant-coefficient $n^{th}$-order ODE?

1 vote
2 answers
3k views

Prove that $f:\mathbb{R}\times\mathbb{Z}\rightarrow\mathbb{R}$, $f(x,y)=\frac{2}{\pi}\arctan x+2y$ is injective