User Daniel Schepler - Mathematics Stack Exchange

55 votes

Accepted

Is "taking a limit" a function? Is it a procedure? A ternary operation?

answered Feb 1, 2020 at 16:44

23 votes

Do nonconstructive proofs of isomorphism exist?

answered Aug 24, 2022 at 21:45

20 votes

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Is a dense set always infinite?

answered Feb 3, 2019 at 16:17

19 votes

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Is there a proof that performing an operation on both sides of an equation preserves equality?

answered Aug 14, 2018 at 18:07

18 votes

What is an intuitive Geometrical explanation of a "sheaf?"

answered Feb 8, 2018 at 19:11

18 votes

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Exact value of $\arctan(2)$

answered Sep 12, 2017 at 23:20

13 votes

Interval of convergence of $\sum_{n=1}^\infty x^{\ln(n)}$.

answered Sep 11, 2017 at 4:35

13 votes

Accepted

Rewrite $f(x,y) = 1-x^2y^2$ as a product $g(x) \cdot h(y)$

answered Oct 19, 2018 at 17:55

12 votes

What exactly is a function?

answered Jul 26, 2018 at 0:50

10 votes

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If $X \times Y$ is Separable, are $X, Y$ Separable?

answered Jun 29, 2018 at 21:29

10 votes

Accepted

Strong Induction Requires No Base Case?

answered Oct 19, 2017 at 0:40

10 votes

why is the definition of the determinant so weird?

answered Nov 15, 2016 at 0:00

10 votes

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Are inf and sup continuous functionals in general?

answered Mar 16, 2023 at 17:13

10 votes

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Is every topos a De Morgan topos?

answered May 25, 2023 at 16:35

9 votes

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How to prove binomial coefficient $ {2^n \choose k} $ is even number?

answered Jan 25, 2019 at 23:21

9 votes

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Is an ideal where all elements have $x^m=0$ nilpotent?

answered Jan 28, 2020 at 16:22

8 votes

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Prove that $(1-\sqrt{-5})\otimes(1+\sqrt{-5})\not=2\otimes 3$ in a specific tensor product.

answered Jan 24, 2020 at 20:01

8 votes

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Does the sum $\sum_{n = 1} ^\infty \frac{\sqrt {n!}} {(3+\sqrt 1)(3+\sqrt 2)...(3+\sqrt n)} $ converge or diverge?

answered Jul 22, 2019 at 16:35

8 votes

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Show that the operator has a chain of invariant subspaces.

answered Oct 15, 2017 at 15:04

8 votes

Area of a square inside a square created by connecting point-opposite midpoint

answered Nov 14, 2017 at 0:36

8 votes

Calculating the square root of 2

answered Sep 14, 2018 at 22:43

8 votes

Non-natural transformation example

answered May 8, 2018 at 22:14

8 votes

Accepted

$\lim_{n\to\infty}\left\{n\sum_{k=1}^n\frac{1}{k^5}\right\}$

answered Jun 24 at 19:32

8 votes

What concretely does it mean to "do mathematics in a topos X"?

answered Jul 18 at 15:32

7 votes

Accepted

Find the generating function for $a_n=\sum_{k=0}^{n} 3^{k}(n-k), n\geq0$.

answered Mar 8 at 22:49

7 votes

Criteria for inclusions in co-product to be monos

answered May 10, 2018 at 22:26

7 votes

Accepted

Let $f\in C^2(\mathbb R)$. I have to prove that there is $c\in [a,b]$ s.t. $f(b)=f(a)+f'(a)(b-a)+\frac{f''(c)}{2}(b-a)^2.$

answered Jul 23, 2018 at 21:30

7 votes

Demystifying math: How someone you could have come up with singular homology?

answered Dec 13, 2017 at 23:10

7 votes

Do we have $(f^{-1}(\mathcal O_{\operatorname{Spec}A}))(\operatorname{Spec}B)=A$?

answered Dec 14, 2017 at 23:26

7 votes

Reason why in Gaussian integers, norm divisibility may not lead to divisibility.

answered Dec 30, 2017 at 1:47

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621 Answers

Is "taking a limit" a function? Is it a procedure? A ternary operation?

Do nonconstructive proofs of isomorphism exist?

Is a dense set always infinite?

Is there a proof that performing an operation on both sides of an equation preserves equality?

What is an intuitive Geometrical explanation of a "sheaf?"

Exact value of $\arctan(2)$

Interval of convergence of $\sum_{n=1}^\infty x^{\ln(n)}$.

Rewrite $f(x,y) = 1-x^2y^2$ as a product $g(x) \cdot h(y)$

What exactly is a function?

If $X \times Y$ is Separable, are $X, Y$ Separable?

Strong Induction Requires No Base Case?

why is the definition of the determinant so weird?

Are inf and sup continuous functionals in general?

Is every topos a De Morgan topos?

How to prove binomial coefficient $ {2^n \choose k} $ is even number?

Is an ideal where all elements have $x^m=0$ nilpotent?

Prove that $(1-\sqrt{-5})\otimes(1+\sqrt{-5})\not=2\otimes 3$ in a specific tensor product.

Does the sum $\sum_{n = 1} ^\infty \frac{\sqrt {n!}} {(3+\sqrt 1)(3+\sqrt 2)...(3+\sqrt n)} $ converge or diverge?

Show that the operator has a chain of invariant subspaces.

Area of a square inside a square created by connecting point-opposite midpoint

Calculating the square root of 2

Non-natural transformation example

$\lim_{n\to\infty}\left\{n\sum_{k=1}^n\frac{1}{k^5}\right\}$

What concretely does it mean to "do mathematics in a topos X"?

Find the generating function for $a_n=\sum_{k=0}^{n} 3^{k}(n-k), n\geq0$.

Criteria for inclusions in co-product to be monos

Let $f\in C^2(\mathbb R)$. I have to prove that there is $c\in [a,b]$ s.t. $f(b)=f(a)+f'(a)(b-a)+\frac{f''(c)}{2}(b-a)^2.$

Demystifying math: How someone you could have come up with singular homology?

Do we have $(f^{-1}(\mathcal O_{\operatorname{Spec}A}))(\operatorname{Spec}B)=A$?

Reason why in Gaussian integers, norm divisibility may not lead to divisibility.