Question

Every linear operator $T:X \to Y$ on a finite-dimensional normed space is bounded

score 6.1k · Answer 1 · 2026-04-11 11:57:05

6.1k

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Every linear operator $T:X \to Y$ on a finite-dimensional normed space is bounded

Published on 11 Apr 2026 - 11:57

score 1.1k · Answer 2 · 2026-04-14 12:15:42

1.1k

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Proving a space is Hausdorff if $f$ is continuous and bijective

Published on 14 Apr 2026 - 12:15

score 86 · Answer 3 · 2026-04-16 08:27:08

86

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If $\lim_{n\to \infty}s_n = \infty$ then also $\lim_{n\to \infty}\sqrt s_n = \infty$

Published on 16 Apr 2026 - 8:27

score 104 · Answer 4 · 2026-04-17 06:18:26

104

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Prove that $W_1 \cup W_2$ is subspace of $V$ if and only if $W_1 \subseteq W_2$ or $W_2 \subseteq W_1$

Published on 17 Apr 2026 - 6:18

score 86 · Answer 5 · 2026-04-10 11:42:26

86

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Exercise about multiple integration

Published on 10 Apr 2026 - 11:42

score 267 · Answer 6 · 2026-04-14 23:11:23

267

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If $\sum_{n\geq 1}\frac{a_n}{n}$ converges, then $\lim_{n\rightarrow \infty}\frac{1}{n}\sum_{k=1}^na_k=0$

Published on 14 Apr 2026 - 23:11

score 80 · Answer 7 · 2026-04-14 01:21:04

80

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Integration by parts $3n$ times.

Published on 14 Apr 2026 - 1:21

score 596 · Answer 8 · 2026-04-16 21:34:50

596

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If A and B are compact sets, then A ∩ B is compact.

Published on 16 Apr 2026 - 21:34

score 56 · Answer 9 · 2026-04-14 03:46:51

56

Views

Induction verification: Prove that $2^n < n!$, for all natural numbers $n > 3$

Published on 14 Apr 2026 - 3:46

score 57 · Answer 10 · 2026-04-15 05:57:26

57

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How to write a regular expression over $\{a,b\}$ such that there're at least $3$ occurrences of adjacent different letters?

Published on 15 Apr 2026 - 5:57

score 56 · Answer 11 · 2026-04-15 00:59:15

56

Views

Is $x(1 - 2x) \le \frac{1}{8}$ and further, is $x(1 - ax) \le \frac{1}{4a}$

Published on 15 Apr 2026 - 0:59

score 667 · Answer 12 · 2026-04-14 09:54:09

667

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matrix eigenvalue problem for a skew symmetric matrix of order 5

Published on 14 Apr 2026 - 9:54

score 102 · Answer 13 · 2026-03-26 02:57:43

102

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Conditional distribution of $X_1\mid -\sum\log X_i$ where $X_i$'s are i.i.d with pdf $\theta x^{\theta-1}$

Published on 26 Mar 2026 - 2:57

score 202 · Answer 14 · 2026-04-15 21:49:25

202

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Partial derivative being $0$ implies non-dependence on that coordinate for $f: U \rightarrow \mathbb{R}$ and $U \in \mathbb{R}^n$ open and convex

Published on 15 Apr 2026 - 21:49

score 66 · Answer 15 · 2026-04-17 03:43:06

66

Views

Prove: $m^(E+x_0)=m^(E)$

Published on 17 Apr 2026 - 3:43

List Question

Every linear operator $T:X \to Y$ on a finite-dimensional normed space is bounded

Proving a space is Hausdorff if $f$ is continuous and bijective

If $\lim_{n\to \infty}s_n = \infty$ then also $\lim_{n\to \infty}\sqrt s_n = \infty$

Prove that $W_1 \cup W_2$ is subspace of $V$ if and only if $W_1 \subseteq W_2$ or $W_2 \subseteq W_1$

Exercise about multiple integration

If $\sum_{n\geq 1}\frac{a_n}{n}$ converges, then $\lim_{n\rightarrow \infty}\frac{1}{n}\sum_{k=1}^na_k=0$

Integration by parts $3n$ times.

If A and B are compact sets, then A ∩ B is compact.

Induction verification: Prove that $2^n < n!$, for all natural numbers $n > 3$

How to write a regular expression over $\{a,b\}$ such that there're at least $3$ occurrences of adjacent different letters?

Is $x(1 - 2x) \le \frac{1}{8}$ and further, is $x(1 - ax) \le \frac{1}{4a}$

matrix eigenvalue problem for a skew symmetric matrix of order 5

Conditional distribution of $X_1\mid -\sum\log X_i$ where $X_i$'s are i.i.d with pdf $\theta x^{\theta-1}$

Partial derivative being $0$ implies non-dependence on that coordinate for $f: U \rightarrow \mathbb{R}$ and $U \in \mathbb{R}^n$ open and convex

Prove: $m^(E+x_0)=m^(E)$

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