Question

Brezis' exercise 6.10.2: prove that $N(I-T) = \{0\} \iff R(I-T) = E$

score 33 · Answer 1 · 2026-05-15 16:07:07

33

Views

Brezis' exercise 6.10.2: prove that $N(I-T) = \{0\} \iff R(I-T) = E$

Published on 15 May 2026 - 16:07

score 95 · Answer 2 · 2026-04-15 20:45:45

95

Views

Determine all subgroups of $\mathbb{R}^*$ (nonzero reals under multiplication) of index 2

Published on 15 Apr 2026 - 20:45

score 81 · Answer 3 · 2026-04-17 05:34:24

81

Views

Show that $A \cap B$ is open in $\Bbb R$ if and only if there exists $X \subseteq \Bbb R$ such that $A \cap B = A \cap X$ as follows.

Published on 17 Apr 2026 - 5:34

score 23 · Answer 4 · 2026-05-04 20:10:40

23

Views

Regarding units modulo $n$

Published on 04 May 2026 - 20:10

score 111 · Answer 5 · 2026-04-16 06:16:20

111

Views

Check that $\sum_{n=0}^{\infty}(1-x^2)x^n$ uniformly converges on $[0;1]$

Published on 16 Apr 2026 - 6:16

score 113 · Answer 6 · 2026-04-11 23:06:07

113

Views

Prove that $\int_{E}fd\mu = 0\implies f= 0$ a.e with $f$ a positive measurable function

Published on 11 Apr 2026 - 23:06

score 382 · Answer 7 · 2026-04-16 01:37:51

382

Views

Convergence in distribution for $Y_n=\min(X_1,X_2,\ldots,X_n)$ with i.i.d. Uniform$(0,1)$ random variables

Published on 16 Apr 2026 - 1:37

score 140 · Answer 8 · 2026-04-12 19:29:12

140

Views

Can we use series expansion to evaluate $\lim_{x\to\infty}\frac{\cos x+\sin x}{x^2}?$

Published on 12 Apr 2026 - 19:29

score 42 · Answer 9 · 2026-04-13 11:57:27

42

Views

Check if the bilinear form given in the standard basis gives some dot product to $\mathbb R^3$

Published on 13 Apr 2026 - 11:57

score 47 · Answer 10 · 2026-05-15 16:06:26

47

Views

Brezis' exercise 6.10.3: $\dim N(I-T) = \dim N(I-T^*)$

Published on 15 May 2026 - 16:06

score 24 · Answer 11 · 2026-04-15 19:40:25

24

Views

Exercises solutions for "Game Physics Development" by Ian Millington

Published on 15 Apr 2026 - 19:40

score 200 · Answer 12 · 2026-05-16 01:17:02

200

Views

If $f$ and $g$ are coprime, then $Z(f) \cap Z(g)$ is finite (in projective space $\Bbb P^2$).

Published on 16 May 2026 - 1:17

score 126 · Answer 13 · 2026-04-13 09:40:42

126

Views

Proof that $x^2$ is not uniformly continuous on $\mathbb{R}$

Published on 13 Apr 2026 - 9:40

score 52 · Answer 14 · 2026-04-15 16:28:46

52

Views

Brezis' exercise 6.11: a closed subspace of $C(K, \mathbb R)$

Published on 15 Apr 2026 - 16:28

score 34 · Answer 15 · 2026-04-13 21:00:03

34

Views

Proof of Euler's theorem for positively homogeneous functions $\Bbb R^2\setminus\{(0,0)\}\to\Bbb R$?

Published on 13 Apr 2026 - 21:00

List Question

Brezis' exercise 6.10.2: prove that $N(I-T) = \{0\} \iff R(I-T) = E$

Determine all subgroups of $\mathbb{R}^*$ (nonzero reals under multiplication) of index 2

Show that $A \cap B$ is open in $\Bbb R$ if and only if there exists $X \subseteq \Bbb R$ such that $A \cap B = A \cap X$ as follows.

Regarding units modulo $n$

Check that $\sum_{n=0}^{\infty}(1-x^2)x^n$ uniformly converges on $[0;1]$

Prove that $\int_{E}fd\mu = 0\implies f= 0$ a.e with $f$ a positive measurable function

Convergence in distribution for $Y_n=\min(X_1,X_2,\ldots,X_n)$ with i.i.d. Uniform$(0,1)$ random variables

Can we use series expansion to evaluate $\lim_{x\to\infty}\frac{\cos x+\sin x}{x^2}?$

Check if the bilinear form given in the standard basis gives some dot product to $\mathbb R^3$

Brezis' exercise 6.10.3: $\dim N(I-T) = \dim N(I-T^*)$

Exercises solutions for "Game Physics Development" by Ian Millington

If $f$ and $g$ are coprime, then $Z(f) \cap Z(g)$ is finite (in projective space $\Bbb P^2$).

Proof that $x^2$ is not uniformly continuous on $\mathbb{R}$

Brezis' exercise 6.11: a closed subspace of $C(K, \mathbb R)$

Proof of Euler's theorem for positively homogeneous functions $\Bbb R^2\setminus\{(0,0)\}\to\Bbb R$?

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