List questions from examples-counterexamples

Published on 28 Mar 2026 - 1:48

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Example of a function whose second derivative does not exist but limiting formula for the second derivative holds

Published on 10 Jul 2020 - 14:01

1.2k

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Abel's test for improper integrals with only integrable functions

Published on 10 Jul 2020 - 15:47

465

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Decreasing and bounded product of Lipschitz functions is Lipschitz

Published on 27 Mar 2026 - 13:27

193

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Prove or disprove: $A$ is a subgroup of $G$ if and only if $AA=A$.

Published on 26 Mar 2026 - 8:00

102

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Is $(A+B)$ necessarily singular?

Published on 02 Apr 2026 - 21:45

339

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Conjecture about rational numbers

Published on 23 Feb 2026 - 22:53

93

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Does local convexity imply global convexity around a minimum?

Published on 25 Mar 2026 - 12:49

72

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Counterexample to finiteness of KL divergence?

Published on 23 Feb 2026 - 4:39

112

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prove that there is at least one pentagon where you cannot get a triangle from any diagonals (a pentagon may not be convex)

Published on 14 Jul 2020 - 8:44

586

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Are there sets where it cannot possibly have a metric on it?

Published on 14 Jul 2020 - 18:43

242

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Convergent sequence and Hausdorff space

Published on 26 Mar 2026 - 4:29

324

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Does $\ker T\cap {\rm Im}\,T=\{0\}$ imply $V=\ker T\oplus{\rm Im}\,T$?

Published on 28 Mar 2026 - 5:22

407

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Pretty conjecture $x^{\left(\frac{y}{x}\right)^n}+y^{\left(\frac{x}{y}\right)^n}\leq 1$

Published on 27 Mar 2026 - 12:30

182

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Bound on truncated trigonometric polynomial

Published on 27 Mar 2026 - 8:39

List Question

Localization of a infinite sum of ideals not equal to infinite sum of localized ideals

Example of a function whose second derivative does not exist but limiting formula for the second derivative holds

Abel's test for improper integrals with only integrable functions

Decreasing and bounded product of Lipschitz functions is Lipschitz

Prove or disprove: $A$ is a subgroup of $G$ if and only if $AA=A$.

Is $(A+B)$ necessarily singular?

Conjecture about rational numbers

Does local convexity imply global convexity around a minimum?

Counterexample to finiteness of KL divergence?

prove that there is at least one pentagon where you cannot get a triangle from any diagonals (a pentagon may not be convex)

Are there sets where it cannot possibly have a metric on it?

Convergent sequence and Hausdorff space

Does $\ker T\cap {\rm Im}\,T=\{0\}$ imply $V=\ker T\oplus{\rm Im}\,T$?

Pretty conjecture $x^{\left(\frac{y}{x}\right)^n}+y^{\left(\frac{x}{y}\right)^n}\leq 1$

Bound on truncated trigonometric polynomial

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