Question

Find all $f:\mathbb{Z} ^2 \to \mathbb{Z}$, such that $\forall p(x) \in P[\mathbb{Z}]: \forall a,b \in \mathbb{Z}: f(p(a),p(b)) = p(f(a,b))$

score 46 · Answer 1 · 2019-12-15 20:07:03

46

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Find all $f:\mathbb{Z} ^2 \to \mathbb{Z}$, such that $\forall p(x) \in P[\mathbb{Z}]: \forall a,b \in \mathbb{Z}: f(p(a),p(b)) = p(f(a,b))$

Published on 15 Dec 2019 - 20:07

score 123 · Answer 2 · 2026-03-26 03:18:51

123

Views

Rosser's trick practice exam question

Published on 26 Mar 2026 - 3:18

score 718 · Answer 3 · 2026-03-28 00:49:16

718

Views

If composition of homomorphisms is an isomorphism, then the constituent homomorphisms are also isomorphisms

Published on 28 Mar 2026 - 0:49

score 277 · Answer 4 · 2019-12-16 01:26:15

277

Views

if $\|f\|_p \le C$ for all $p \ge 1$, then $f \in L^\infty$.

Published on 16 Dec 2019 - 1:26

score 102 · Answer 5 · 2019-12-16 03:24:27

102

Views

Contractibility of X implies every point is a deformation retract

Published on 16 Dec 2019 - 3:24

score 965 · Answer 6 · 2026-03-29 03:36:31

965

Views

Prove if $u,v,w$ linearly independent then ${\{u+v+w,v-w,2w}\}$ linearly independent

Published on 29 Mar 2026 - 3:36

score 736 · Answer 7 · 2019-12-16 12:25:39

736

Views

If every map from $S^1$ to a path-connected space X is homotopic to the constant map, then every map $S^1 \to X$ extends to a map $D^2 \to X$

Published on 16 Dec 2019 - 12:25

score 157 · Answer 8 · 2019-12-16 12:51:13

157

Views

Prove that $\mathbb{Q}\times \mathbb{Z_2}$ not isomorphic to $\mathbb{Q}$

Published on 16 Dec 2019 - 12:51

score 158 · Answer 9 · 2019-12-16 13:35:58

158

Views

Find the total number of 7-digit

Published on 16 Dec 2019 - 13:35

score 38 · Answer 10 · 2019-12-16 13:55:19

38

Views

$E_{n,k}= \bigcup_{m\ge n} \Big\{x : |f_m(x)-f(x)|>\frac{1}{k}\Big\}$.Show that $\lim_{n\to \infty}m(E_{n,k})=0$

Published on 16 Dec 2019 - 13:55

score 36 · Answer 11 · 2019-12-16 14:48:18

36

Views

Calculate double integral using polar coordinates

Published on 16 Dec 2019 - 14:48

score 139 · Answer 12 · 2019-12-16 15:54:12

139

Views

Showing that $[\mathbb{Q}(\sqrt{p},\sqrt{q}):\mathbb{Q}]=4$

Published on 16 Dec 2019 - 15:54

score 240 · Answer 13 · 2026-03-26 09:49:53

240

Views

In triangle $ABC$, find maximum value of $\sin A \cos B + \sin B \cos C + \sin C \cos A$

Published on 26 Mar 2026 - 9:49

score 201 · Answer 14 · 2019-12-16 17:56:14

201

Views

Proving $\mathscr P(A)\cap\mathscr P(B)=\mathscr P(A\cap B)$ is my proof valid?

Published on 16 Dec 2019 - 17:56

score 133 · Answer 15 · 2019-12-16 22:30:13

133

Views

How to show that $\lim_{n\to\infty}\mathbb{P}\left(\bigg|\frac{1}{n}S_n-f(n)\bigg|>\varepsilon\right)=0$

Published on 16 Dec 2019 - 22:30

List Question

Find all $f:\mathbb{Z} ^2 \to \mathbb{Z}$, such that $\forall p(x) \in P[\mathbb{Z}]: \forall a,b \in \mathbb{Z}: f(p(a),p(b)) = p(f(a,b))$

Rosser's trick practice exam question

If composition of homomorphisms is an isomorphism, then the constituent homomorphisms are also isomorphisms

if $\|f\|_p \le C$ for all $p \ge 1$, then $f \in L^\infty$.

Contractibility of X implies every point is a deformation retract

Prove if $u,v,w$ linearly independent then ${\{u+v+w,v-w,2w}\}$ linearly independent

If every map from $S^1$ to a path-connected space X is homotopic to the constant map, then every map $S^1 \to X$ extends to a map $D^2 \to X$

Prove that $\mathbb{Q}\times \mathbb{Z_2}$ not isomorphic to $\mathbb{Q}$

Find the total number of 7-digit

$E_{n,k}= \bigcup_{m\ge n} \Big\{x : |f_m(x)-f(x)|>\frac{1}{k}\Big\}$.Show that $\lim_{n\to \infty}m(E_{n,k})=0$

Calculate double integral using polar coordinates

Showing that $[\mathbb{Q}(\sqrt{p},\sqrt{q}):\mathbb{Q}]=4$

In triangle $ABC$, find maximum value of $\sin A \cos B + \sin B \cos C + \sin C \cos A$

Proving $\mathscr P(A)\cap\mathscr P(B)=\mathscr P(A\cap B)$ is my proof valid?

How to show that $\lim_{n\to\infty}\mathbb{P}\left(\bigg|\frac{1}{n}S_n-f(n)\bigg|>\varepsilon\right)=0$

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