Question

Sketch $M=\{re^{i\phi}:r\in(1,2],\phi\in[0,\pi)\}$ and give its closure $\overline{M}$. Is $M$ compact?

score 48 · Answer 1 · 2026-04-15 21:01:34

48

Views

Sketch $M=\{re^{i\phi}:r\in(1,2],\phi\in[0,\pi)\}$ and give its closure $\overline{M}$. Is $M$ compact?

Published on 15 Apr 2026 - 21:01

score 473 · Answer 2 · 2026-04-15 10:57:42

473

Views

Why is the rule of substitution of functions an axiom?

Published on 15 Apr 2026 - 10:57

score 110 · Answer 3 · 2026-04-13 23:34:44

110

Views

Let $K\subseteq\mathbb{C}$ be compact and non-empty. Show there exists a $z\in K$ such that $|z|=\inf\{|w|:w\in K\}$.

Published on 13 Apr 2026 - 23:34

score 32 · Answer 4 · 2026-04-10 21:07:02

32

Views

Computing a limit in a complex integral

Published on 10 Apr 2026 - 21:07

score 281 · Answer 5 · 2026-04-16 06:46:54

281

Views

Showing a list of polynomials is linearly dependent in $\mathcal{P}_m(\mathbb{F})$

Published on 16 Apr 2026 - 6:46

score 43 · Answer 6 · 2026-04-14 09:00:31

43

Views

Prove that $\int_{a}^{b} h(x)dx = \lim_{k\to\infty} \sum_{j=1}^{k} h(x^{k}_{j})\frac{b-a}{k}$ using given intermediate points.

Published on 14 Apr 2026 - 9:00

score 130 · Answer 7 · 2026-04-14 06:24:40

130

Views

Alternative proof limit definition is equivalent to sequence limit definition (Rudin 4.2)

Published on 14 Apr 2026 - 6:24

score 414 · Answer 8 · 2026-04-16 07:48:34

414

Views

$\forall a,b \in {\mathbb R^+}$: if $a=b$ then $\sqrt a =\sqrt b$

Published on 16 Apr 2026 - 7:48

score 53 · Answer 9 · 2026-04-11 20:23:10

53

Views

Error in proof of Fourier rotation theorem

Published on 11 Apr 2026 - 20:23

score 791 · Answer 10 · 2026-04-09 05:31:19

791

Views

Is my proof correct on how $k$ must be a power of $2$? Are there other proofs?

Published on 09 Apr 2026 - 5:31

score 33 · Answer 11 · 2026-04-15 12:42:26

33

Views

Proving lemmas during construction of non-measurable sets.

Published on 15 Apr 2026 - 12:42

score 61 · Answer 12 · 2026-04-14 07:39:03

61

Views

If $C\subseteq [0,1]$ is infinite, $\exists a$ s.t. $C\cap[a,1]$ is infinite

Published on 14 Apr 2026 - 7:39

score 2.8k · Answer 13 · 2026-04-15 17:41:33

2.8k

Views

Show that $ \sqrt{2 + \sqrt{2 + \sqrt{2 + 2 \cos 8\theta}}} = 2 \cos \theta$

Published on 15 Apr 2026 - 17:41

score 87 · Answer 14 · 2026-04-15 16:05:00

87

Views

Is $\sum_{i=1}^{n-1}i^{n-1}\equiv -1\pmod {2n}\Leftrightarrow \text{$n$ is prime }\equiv 3\pmod 4$?

Published on 15 Apr 2026 - 16:05

score 1k · Answer 15 · 2026-04-14 08:01:18

1k

Views

Proving that there exists a vector that makes a linear system inconsistent

Published on 14 Apr 2026 - 8:01

List Question

Sketch $M=\{re^{i\phi}:r\in(1,2],\phi\in[0,\pi)\}$ and give its closure $\overline{M}$. Is $M$ compact?

Why is the rule of substitution of functions an axiom?

Let $K\subseteq\mathbb{C}$ be compact and non-empty. Show there exists a $z\in K$ such that $|z|=\inf\{|w|:w\in K\}$.

Computing a limit in a complex integral

Showing a list of polynomials is linearly dependent in $\mathcal{P}_m(\mathbb{F})$

Prove that $\int_{a}^{b} h(x)dx = \lim_{k\to\infty} \sum_{j=1}^{k} h(x^{k}_{j})\frac{b-a}{k}$ using given intermediate points.

Alternative proof limit definition is equivalent to sequence limit definition (Rudin 4.2)

$\forall a,b \in {\mathbb R^+}$: if $a=b$ then $\sqrt a =\sqrt b$

Error in proof of Fourier rotation theorem

Is my proof correct on how $k$ must be a power of $2$? Are there other proofs?

Proving lemmas during construction of non-measurable sets.

If $C\subseteq [0,1]$ is infinite, $\exists a$ s.t. $C\cap[a,1]$ is infinite

Show that $ \sqrt{2 + \sqrt{2 + \sqrt{2 + 2 \cos 8\theta}}} = 2 \cos \theta$

Is $\sum_{i=1}^{n-1}i^{n-1}\equiv -1\pmod {2n}\Leftrightarrow \text{$n$ is prime }\equiv 3\pmod 4$?

Proving that there exists a vector that makes a linear system inconsistent

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