List questions from examples-counterexamples

Published on 30 May 2014 - 13:51

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Extraneous solutions.

Published on 31 May 2014 - 9:12

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Applications of the identity $ab + \left(\frac{a+b}{2} - b\right)^2 = \left(\frac{a+b}{2}\right)^2$

Published on 01 Jun 2014 - 2:45

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Question about a counterexample concerning compact operators

Published on 26 Mar 2026 - 9:25

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Counterexample to Marcinkiewicz

Published on 02 Jun 2014 - 9:53

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Question about compact operator

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Infinite abelian group counterexample

Published on 25 Mar 2026 - 12:52

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Closure of Integers under multiplication and rational exponentiation

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A set that is a countable intersection of open and dense sets but not open.

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The topology on $X/{\sim}\times X/{\sim}$ is not induced by $\pi\times\pi$.

Published on 26 Mar 2026 - 11:18

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Example of a subgroup of index two which contains a non square element

Published on 04 Jun 2014 - 21:32

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Can someone give an example of a function that is not Henstock-Kurzweil/gauge integrable?

Published on 25 Mar 2026 - 6:29

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$\mathcal{C}^\infty$ strictly monotone function $\lim f(x) = 0$, but $\lim f^\prime(x) \ne 0$

Published on 05 Jun 2014 - 23:37

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Counterexample for converse about measurable sections

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If $a, b$ are relatively prime proof and $ab$ is a perfect square, so are $a$, $b$

Published on 28 Mar 2026 - 20:58

List Question

Problem on Convergence of random series

Extraneous solutions.

Applications of the identity $ab + \left(\frac{a+b}{2} - b\right)^2 = \left(\frac{a+b}{2}\right)^2$

Question about a counterexample concerning compact operators

Counterexample to Marcinkiewicz

Question about compact operator

Infinite abelian group counterexample

Closure of Integers under multiplication and rational exponentiation

A set that is a countable intersection of open and dense sets but not open.

The topology on $X/{\sim}\times X/{\sim}$ is not induced by $\pi\times\pi$.

Example of a subgroup of index two which contains a non square element

Can someone give an example of a function that is not Henstock-Kurzweil/gauge integrable?

$\mathcal{C}^\infty$ strictly monotone function $\lim f(x) = 0$, but $\lim f^\prime(x) \ne 0$

Counterexample for converse about measurable sections

If $a, b$ are relatively prime proof and $ab$ is a perfect square, so are $a$, $b$

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