Question

Is there a function that's continuous and has all directional derivatives as a linear function of direction, but still fails to be differentiable?

score 2.3k · Answer 1 · 2015-10-25 17:04:54

2.3k

Views

Is there a function that's continuous and has all directional derivatives as a linear function of direction, but still fails to be differentiable?

Published on 25 Oct 2015 - 17:04

score 386 · Answer 2 · 2026-04-11 02:14:31

386

Views

conjecture in probability, assume conjecture to be true

Published on 11 Apr 2026 - 2:14

score 2.6k · Answer 3 · 2015-10-26 05:16:52

2.6k

Views

Give an example of a nonabelian group in which a product of elements of finite order can have infinite order.

Published on 26 Oct 2015 - 5:16

score 1.5k · Answer 4 · 2026-03-30 00:24:41

Examples of bi-implications ($\Leftrightarrow$) where the $\Rightarrow$ direction is used in the proof of the $\Leftarrow$ direction.

score 56 · Answer 5 · 2026-04-03 10:05:00

56

Views

Disproving Differentiable Functions with Counter Examples

Published on 03 Apr 2026 - 10:05

score 267 · Answer 6 · 2015-10-28 03:37:53

267

Views

Give an example of sets $X,Y$ and functions $f:X→Y$ and $g:Y →X$ such that $g \circ f = id_X$

Published on 28 Oct 2015 - 3:37

score 1.5k · Answer 7 · 2015-10-28 03:38:39

1.5k

Views

Disconnectedness, completeness and compactness.

Published on 28 Oct 2015 - 3:38

score 68 · Answer 8 · 2026-03-28 04:37:39

68

Views

Counter-examples in representations of associative algebra

Published on 28 Mar 2026 - 4:37

score 84 · Answer 9 · 2015-11-02 10:22:31

84

Views

Finding $a_n\to 0$ such that $\sum a_n/n$ diverges

Published on 02 Nov 2015 - 10:22

score 6k · Answer 10 · 2015-11-03 09:01:26

6k

Views

Example of an unbounded sequence whose convergent subsequences converge to same limit

Published on 03 Nov 2015 - 9:01

score 158 · Answer 11 · 2026-04-05 17:35:36

158

Views

$E(X_n)=E(X_{n-1})=\ldots=E(X_0)\nRightarrow (X_n)_n$ is Martingale

Published on 05 Apr 2026 - 17:35

score 189 · Answer 12 · 2015-11-03 16:23:14

189

Views

Counterexample to proposition on $\sigma$-algebras

Published on 03 Nov 2015 - 16:23

score 73 · Answer 13 · 2026-04-04 13:40:25

73

Views

Isomorphism $\phi:G\to G\times G$

Published on 04 Apr 2026 - 13:40

score 156 · Answer 14 · 2026-03-28 17:04:57

156

Views

counter example - affine space

Published on 28 Mar 2026 - 17:04

score 389 · Answer 15 · 2026-04-10 10:55:00

389

Views

a dense set in plane

Published on 10 Apr 2026 - 10:55

List Question

Is there a function that's continuous and has all directional derivatives as a linear function of direction, but still fails to be differentiable?

conjecture in probability, assume conjecture to be true

Give an example of a nonabelian group in which a product of elements of finite order can have infinite order.

Examples of bi-implications ($\Leftrightarrow$) where the $\Rightarrow$ direction is used in the proof of the $\Leftarrow$ direction.

Disproving Differentiable Functions with Counter Examples

Give an example of sets $X,Y$ and functions $f:X→Y$ and $g:Y →X$ such that $g \circ f = id_X$

Disconnectedness, completeness and compactness.

Counter-examples in representations of associative algebra

Finding $a_n\to 0$ such that $\sum a_n/n$ diverges

Example of an unbounded sequence whose convergent subsequences converge to same limit

$E(X_n)=E(X_{n-1})=\ldots=E(X_0)\nRightarrow (X_n)_n$ is Martingale

Counterexample to proposition on $\sigma$-algebras

Isomorphism $\phi:G\to G\times G$

counter example - affine space

a dense set in plane

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