List questions from examples-counterexamples

Published on 14 Apr 2026 - 8:16

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$P_2$-groups are not always $P_3$-groups : a group by Blackburn

Published on 14 Apr 2026 - 17:07

119

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Suppose $R$ is a relation on $A$, and $S$ is a relation on $\mathscr P(A)$. If $R$ is transitive, must $S$ be transitive?

Published on 14 Apr 2026 - 13:25

142

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Counterexample for Cauchy Sequence

Published on 12 Apr 2026 - 7:32

158

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A set very different from itself

Published on 12 Apr 2026 - 6:46

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lebesgue integral and counterexample

Published on 13 Apr 2026 - 21:46

1k

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Can an $R$-module have bases of different cardinality?

Published on 12 Apr 2026 - 12:49

546

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Natural examples of removable discontinuities?

Published on 09 Apr 2026 - 1:58

296

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Can a sequence contain an undefined term (e.g. a member acquired by dividing a number by zero)?

Published on 13 Apr 2026 - 21:34

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sigmoid $\circ$ sigmoid = sigmoid?

Published on 15 Apr 2026 - 11:21

744

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Examples for topological vector space

Published on 14 Apr 2026 - 6:25

682

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Does a counterexample always disprove a conjecture?

Published on 11 Apr 2026 - 20:14

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Counterexample for $(ab)^2=a^2b^2$

Published on 16 Apr 2026 - 19:52

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Example of a sequence $(f_n)_n$, such that $(f_ n')_n$ converges uniformly, but $(f_n)_n$ doesn't converge in any point.

Published on 16 Apr 2026 - 8:18

110

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Can one find a surjection $f:D\to{\bf C}$ such that $f$ is not a rational function?

Published on 11 Apr 2026 - 16:20

List Question

What is the smallest $20$ digit number with at least $13$ distinct prime factors?

$P_2$-groups are not always $P_3$-groups : a group by Blackburn

Suppose $R$ is a relation on $A$, and $S$ is a relation on $\mathscr P(A)$. If $R$ is transitive, must $S$ be transitive?

Counterexample for Cauchy Sequence

A set very different from itself

lebesgue integral and counterexample

Can an $R$-module have bases of different cardinality?

Natural examples of removable discontinuities?

Can a sequence contain an undefined term (e.g. a member acquired by dividing a number by zero)?

sigmoid $\circ$ sigmoid = sigmoid?

Examples for topological vector space

Does a counterexample always disprove a conjecture?

Counterexample for $(ab)^2=a^2b^2$

Example of a sequence $(f_n)_n$, such that $(f_ n')_n$ converges uniformly, but $(f_n)_n$ doesn't converge in any point.

Can one find a surjection $f:D\to{\bf C}$ such that $f$ is not a rational function?

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