List questions from examples-counterexamples

Published on 05 May 2026 - 15:29

231

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Seeking an example of Schwartz function $f$ such that $ \int_{\bf R}\left|\frac{f(x-y)}{y}\right|\ dy=\infty$

Published on 29 Apr 2026 - 12:07

81

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Inner Product Uniqueness

Published on 06 May 2026 - 7:27

969

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Metric on a linear space is induced by norm if and only if the metric is homogeneous and translation invariant

Published on 07 May 2026 - 7:38

83

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Why do I need boundedness for a a closed subset of $\mathbb{R}$ to have a maximum?

Published on 06 May 2026 - 10:47

163

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A congruence with the Euler's totient function and number of divisors function

Published on 07 May 2026 - 16:39

156

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Analysis Counterexamples

Published on 07 May 2026 - 7:28

128

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A congruence involving Mersenne numbers

Published on 29 Apr 2026 - 12:08

67

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If $\|\ f \|\ = \max_{|x|=1} |f(x)|$ then is $\|\ f \|\ \|\ f^{-1}\|\ = 1$ for all $f\in \mathcal{L}(\mathbb{R}^m,\mathbb{R}^n)$?

Published on 06 May 2026 - 2:29

1.5k

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Unbounded Feasible Region

Published on 05 May 2026 - 23:28

113

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What would be the function to make a formula false?

Published on 06 May 2026 - 0:36

357

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comparing sup and inf of two sets

Published on 07 May 2026 - 20:39

105

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A Rudin Counterexample. How can we show that $f$ is not measurable without Fubini?

Published on 29 Apr 2026 - 16:59

338

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Giving a counterexample for the extension lemma of smooth functions

Published on 02 May 2026 - 23:49

829

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Example for subgroups $H$ and $K$ where $HK = K H$ and neither $H$ nor $K$ is normal?

Published on 02 May 2026 - 23:51

List Question

A congruence with the Euler's totient function and sum of divisors function

Seeking an example of Schwartz function $f$ such that $ \int_{\bf R}\left|\frac{f(x-y)}{y}\right|\ dy=\infty$

Inner Product Uniqueness

Metric on a linear space is induced by norm if and only if the metric is homogeneous and translation invariant

Why do I need boundedness for a a closed subset of $\mathbb{R}$ to have a maximum?

A congruence with the Euler's totient function and number of divisors function

Analysis Counterexamples

A congruence involving Mersenne numbers

If $\|\ f \|\ = \max_{|x|=1} |f(x)|$ then is $\|\ f \|\ \|\ f^{-1}\|\ = 1$ for all $f\in \mathcal{L}(\mathbb{R}^m,\mathbb{R}^n)$?

Unbounded Feasible Region

What would be the function to make a formula false?

comparing sup and inf of two sets

A Rudin Counterexample. How can we show that $f$ is not measurable without Fubini?

Giving a counterexample for the extension lemma of smooth functions

Example for subgroups $H$ and $K$ where $HK = K H$ and neither $H$ nor $K$ is normal?

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