List questions from examples-counterexamples

Published on 11 Apr 2026 - 4:37

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If $x$ is real number and $x \in \mathbb T$ is then $x^n \in \mathbb T$ for every $n \in \mathbb N$?

Published on 16 Apr 2026 - 10:46

380

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Characterizing bell-shaped curves

Published on 15 Apr 2026 - 1:28

200

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The $n$-th derivative has $n$ zeros. Can such a function be unbounded?

Published on 14 Apr 2026 - 1:16

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Counterexample for ∀x∃y (x=1/y)

Published on 15 Apr 2026 - 4:44

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Has $f'(x)=f(x+1/2)$ non-oscillating solutions?

Published on 14 Apr 2026 - 2:49

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Counterexample $\neg \forall x~(P(x) \to \exists y~Q(x,y)), \forall x~\forall y~(R(x,y) \to (P(y) \vee Q(y,x))) \vdash \cdots$

Published on 16 Apr 2026 - 20:45

799

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Ring $R$ that contains a field $F$ as a subring: Can $R$ not be an integral domain?

Published on 15 Apr 2026 - 12:03

126

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Example for $|gN|<|g|$

Published on 16 Apr 2026 - 11:42

143

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Different Uniformities generating Same Topology

Published on 12 Apr 2026 - 2:59

330

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If $f: \mathbb{R}^n\to \mathbb{R}$ has a continuous derivative at a point

Published on 16 Apr 2026 - 15:51

275

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Give a subspace of $\mathbb R_l \times \mathbb R_l$ that has no countable dense subset [relative to the subspace topology].

Published on 25 Mar 2026 - 20:12

300

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Convergent net which is not Cauchy

Published on 12 Apr 2026 - 2:52

26

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Any Literature Related To Search of Counter Examples?

Published on 15 Apr 2026 - 6:11

385

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Primes dividing sums of squares but not dividing any of summands

Published on 14 Apr 2026 - 12:57

List Question

$L_{\infty}$ norm of slice of a continuous bounded function in $\mathbb{R}^2$

If $x$ is real number and $x \in \mathbb T$ is then $x^n \in \mathbb T$ for every $n \in \mathbb N$?

Characterizing bell-shaped curves

The $n$-th derivative has $n$ zeros. Can such a function be unbounded?

Counterexample for ∀x∃y (x=1/y)

Has $f'(x)=f(x+1/2)$ non-oscillating solutions?

Counterexample $\neg \forall x~(P(x) \to \exists y~Q(x,y)), \forall x~\forall y~(R(x,y) \to (P(y) \vee Q(y,x))) \vdash \cdots$

Ring $R$ that contains a field $F$ as a subring: Can $R$ not be an integral domain?

Example for $|gN|<|g|$

Different Uniformities generating Same Topology

If $f: \mathbb{R}^n\to \mathbb{R}$ has a continuous derivative at a point

Give a subspace of $\mathbb R_l \times \mathbb R_l$ that has no countable dense subset [relative to the subspace topology].

Convergent net which is not Cauchy

Any Literature Related To Search of Counter Examples?

Primes dividing sums of squares but not dividing any of summands

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