List questions from examples-counterexamples

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A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language

Published on 14 Apr 2026 - 22:13

993

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Can you find a domain where $ax+by=1$ has a solution for all $a$ and $b$ relatively prime, but which is not a PID?

Published on 11 Apr 2026 - 5:39

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Perfect set without rationals

Published on 12 Apr 2026 - 18:34

408

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Tips for writing math solutions for others

Published on 09 Apr 2026 - 22:03

11.9k

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Bounded Function Which is Not Riemann Integrable

Published on 09 Apr 2026 - 16:01

779

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Measurable Functions behaviour on $\mathbb{R}^{2}$

Published on 09 Apr 2026 - 18:38

963

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The tree property for non-weakly compact $\kappa$

Published on 14 Apr 2026 - 6:29

8.2k

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Continuous and bounded variation does not imply absolutely continuous

Published on 12 Apr 2026 - 8:03

165

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Continuity of an induced function

Published on 12 Apr 2026 - 9:31

1k

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Why is $T_1$ required for a topological space to be $T_4$?

Published on 14 Apr 2026 - 23:08

7.4k

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Examples of rings with idempotent elements

Published on 16 Apr 2026 - 11:43

10.7k

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Two metrics induce the same topology, but one is complete and the other isn't

Published on 15 Apr 2026 - 8:02

8.2k

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Derived subgroup where not every element is a commutator

Published on 15 Apr 2026 - 9:37

29.3k

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Are Continuous Functions Always Differentiable?

Published on 09 Apr 2026 - 19:31

854

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Basic counterexample re: preimages of ideals

Published on 14 Apr 2026 - 4:35

List Question

A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language

Can you find a domain where $ax+by=1$ has a solution for all $a$ and $b$ relatively prime, but which is not a PID?

Perfect set without rationals

Tips for writing math solutions for others

Bounded Function Which is Not Riemann Integrable

Measurable Functions behaviour on $\mathbb{R}^{2}$

The tree property for non-weakly compact $\kappa$

Continuous and bounded variation does not imply absolutely continuous

Continuity of an induced function

Why is $T_1$ required for a topological space to be $T_4$?

Examples of rings with idempotent elements

Two metrics induce the same topology, but one is complete and the other isn't

Derived subgroup where not every element is a commutator

Are Continuous Functions Always Differentiable?

Basic counterexample re: preimages of ideals

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