Question

With $\Delta=\{(x,\cdots,x)\}$, the set $\{f:X^n\to X^n| \ f\ \text{bijective and}\ f(\Delta)=\Delta\}$ is infinite for all $n\ge1$ if $X$ is infinite

score 52 · Answer 1 · 2018-06-17 23:22:45

52

Views

With $\Delta=\{(x,\cdots,x)\}$, the set $\{f:X^n\to X^n| \ f\ \text{bijective and}\ f(\Delta)=\Delta\}$ is infinite for all $n\ge1$ if $X$ is infinite

Published on 17 Jun 2018 - 23:22

score 50 · Answer 2 · 2026-04-04 02:27:19

50

Views

Valid proof technique? finite-sample argument then convergence in probability

Published on 04 Apr 2026 - 2:27

score 36 · Answer 3 · 2026-03-23 01:45:48

36

Views

Is a left and right simple ring with unity a division ring?

Published on 23 Mar 2026 - 1:45

score 38 · Answer 4 · 2026-03-25 06:50:33

38

Views

Is my understanding correct? (Goodness of Fit question)

Published on 25 Mar 2026 - 6:50

score 137 · Answer 5 · 2026-03-25 06:03:42

137

Views

Proof Verification $ x \ge 0 \wedge x \neq 0 \Rightarrow x > 0$.

Published on 25 Mar 2026 - 6:03

score 245 · Answer 6 · 2026-03-26 19:01:47

245

Views

Prove that $\frac{a_1}{a_9} + \frac{a_2}{a_8}+...\frac{a_9}{a_1} \le 1 + \frac{4(p^2+q^2)}{pq}$

Published on 26 Mar 2026 - 19:01

score 216 · Answer 7 · 2026-03-26 01:28:40

216

Views

Remarkable general proof of substitution rule in integration

Published on 26 Mar 2026 - 1:28

score 69 · Answer 8 · 2026-03-25 15:42:19

69

Views

Approach validation: Model of the diagram of a structure has isomorphic submodel

Published on 25 Mar 2026 - 15:42

score 108 · Answer 9 · 2026-03-29 14:25:24

108

Views

Determine whether $V:=\{x_1,x_2,x_3\in\mathbb{R}^3|2x_1+5x_2=x_3 \}$ is a subspace of $\mathbb{R}^3$

Published on 29 Mar 2026 - 14:25

score 5.5k · Answer 10 · 2026-03-29 10:48:25

5.5k

Views

Determine whether the following sets are subspaces of $\mathbb{R}^3$

Published on 29 Mar 2026 - 10:48

score 79 · Answer 11 · 2018-06-18 19:44:31

79

Views

Proving that $\left(\frac{1}{10^n}\right)_{n=1}^{\infty}$ is $0.1$-steady

Published on 18 Jun 2018 - 19:44

score 323 · Answer 12 · 2026-03-25 08:01:34

323

Views

Prove that a subset of $\mathbb{R}$ with positive outer measure contains almost a whole interval

Published on 25 Mar 2026 - 8:01

score 334 · Answer 13 · 2026-03-25 22:05:09

334

Views

Symmetric Bilinear Form: index of bilinear = the number of positive eigenvalues

Published on 25 Mar 2026 - 22:05

score 617 · Answer 14 · 2026-03-26 17:51:41

617

Views

Countable dimensional normed space incomplete

Published on 26 Mar 2026 - 17:51

score 278 · Answer 15 · 2018-06-19 04:00:34

278

Views

Show that $W_1 \cap W_2 \leq $ the smaller of $n_1$ and $n_2$

Published on 19 Jun 2018 - 4:00

List Question

With $\Delta=\{(x,\cdots,x)\}$, the set $\{f:X^n\to X^n| \ f\ \text{bijective and}\ f(\Delta)=\Delta\}$ is infinite for all $n\ge1$ if $X$ is infinite

Valid proof technique? finite-sample argument then convergence in probability

Is a left and right simple ring with unity a division ring?

Is my understanding correct? (Goodness of Fit question)

Proof Verification $ x \ge 0 \wedge x \neq 0 \Rightarrow x > 0$.

Prove that $\frac{a_1}{a_9} + \frac{a_2}{a_8}+...\frac{a_9}{a_1} \le 1 + \frac{4(p^2+q^2)}{pq}$

Remarkable general proof of substitution rule in integration

Approach validation: Model of the diagram of a structure has isomorphic submodel

Determine whether $V:=\{x_1,x_2,x_3\in\mathbb{R}^3|2x_1+5x_2=x_3 \}$ is a subspace of $\mathbb{R}^3$

Determine whether the following sets are subspaces of $\mathbb{R}^3$

Proving that $\left(\frac{1}{10^n}\right)_{n=1}^{\infty}$ is $0.1$-steady

Prove that a subset of $\mathbb{R}$ with positive outer measure contains almost a whole interval

Symmetric Bilinear Form: index of bilinear = the number of positive eigenvalues

Countable dimensional normed space incomplete

Show that $W_1 \cap W_2 \leq $ the smaller of $n_1$ and $n_2$

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