List questions from examples-counterexamples

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A variation on Giuga's conjecture

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Has miscommunication ever benefited mathematics? Let's list examples.

Published on 19 Mar 2026 - 4:26

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A congruence involving Chebyshev polynomials

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normal doesn't imply paracompact

Published on 17 Mar 2026 - 3:31

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Examples for $\max\{f(x)+g(x)\}\leq \max{f(x)}+ \max{g(x)}$ and $\min\{f(x)+g(x)\}\geq\min{f(x)}$+min{g(x)}.

Published on 20 Mar 2026 - 9:15

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Find $f$ and $g$ that are both $C^1$ with $f(y)=g(y)=0$ and $f'(y)= a g'(y) \neq 0$, but $\lim_{x\to y} \frac{f(x)}{g(x)}$ DNE.

Published on 23 Jan 2018 - 19:28

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Need an example of a category whose products are indexed by these sets.

Published on 25 Mar 2026 - 1:36

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Subset of $\Bbb R$ isomorphic to $\omega+\omega$ and another isomorphic to $\omega\times\omega$

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415

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Counterexamples showing natural density is not a measure

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Counterexamples and Kolmogorov zero-one law (on the convergence of $\sum_{k=1}^\infty (\xi_k - \mathbf{E}(\xi_k))$)

Published on 25 Jan 2018 - 16:28

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towers of 2 and primes, generation s of big primes by iteration of the function $2^{x}$

Published on 22 Mar 2026 - 17:52

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A congruence involving Lucas polynomials

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What is an example of a pi-system that is not a sigma algebra?

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Quasi-components in compact space

Published on 17 Mar 2026 - 1:55

List Question

Counter examples in modal logic

A variation on Giuga's conjecture

Has miscommunication ever benefited mathematics? Let's list examples.

A congruence involving Chebyshev polynomials

normal doesn't imply paracompact

Examples for $\max\{f(x)+g(x)\}\leq \max{f(x)}+ \max{g(x)}$ and $\min\{f(x)+g(x)\}\geq\min{f(x)}$+min{g(x)}.

Find $f$ and $g$ that are both $C^1$ with $f(y)=g(y)=0$ and $f'(y)= a g'(y) \neq 0$, but $\lim_{x\to y} \frac{f(x)}{g(x)}$ DNE.

Need an example of a category whose products are indexed by these sets.

Subset of $\Bbb R$ isomorphic to $\omega+\omega$ and another isomorphic to $\omega\times\omega$

Counterexamples showing natural density is not a measure

Counterexamples and Kolmogorov zero-one law (on the convergence of $\sum_{k=1}^\infty (\xi_k - \mathbf{E}(\xi_k))$)

towers of 2 and primes, generation s of big primes by iteration of the function $2^{x}$

A congruence involving Lucas polynomials

What is an example of a pi-system that is not a sigma algebra?

Quasi-components in compact space

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