Question

Proving $\forall x \in \Bbb R$ and $ \epsilon \gt 0$, $N(x;\epsilon) \backslash \{x\}$ is open.

score 317 · Answer 1 · 2026-04-29 21:16:20

317

Views

Proving $\forall x \in \Bbb R$ and $ \epsilon \gt 0$, $N(x;\epsilon) \backslash \{x\}$ is open.

Published on 29 Apr 2026 - 21:16

score 103 · Answer 2 · 2026-04-16 08:22:11

103

Views

$f$ is a primitive polynomial in $Z[x]$. Show that the intersection of $fQ[x]$ with $Z[x]$ is $fZ[x]$.

Published on 16 Apr 2026 - 8:22

score 116 · Answer 3 · 2026-04-13 02:39:31

116

Views

What's wrong with the following proof that any interval $(a,b) \subset \mathbb{R}$ is connected?

Published on 13 Apr 2026 - 2:39

score 623 · Answer 4 · 2026-04-15 20:56:51

623

Views

Equivalent norms and subsets of open balls PROOF

Published on 15 Apr 2026 - 20:56

score 1.1k · Answer 5 · 2026-04-17 12:10:16

1.1k

Views

Convolution of $L^{1}$ functions is well-defined

Published on 17 Apr 2026 - 12:10

score 63 · Answer 6 · 2026-05-11 05:33:22

63

Views

In showing that if $V=X \oplus Y$, then $X \cap Y = \{0\}$, is writing $v=0+v$ and $v=v+0$ for $v \in X \cap Y$ sufficient?

Published on 11 May 2026 - 5:33

score 69 · Answer 7 · 2026-04-16 14:51:09

69

Views

Let $N$ be a subgroup of a finite group $G$. Show that $|G| = |N| \cdot |G/N|$

Published on 16 Apr 2026 - 14:51

score 313 · Answer 8 · 2026-04-15 12:41:58

313

Views

Let $(G,\odot)$ be a finite group with identity element $e$. Show that for each $g \in G$, there is $k \in \Bbb N^+$ such that $g^k= e$

Published on 15 Apr 2026 - 12:41

score 180 · Answer 9 · 2026-05-10 14:56:32

180

Views

$A\times B \cong B\times A$ in a category $\mathbb{C}$

Published on 10 May 2026 - 14:56

score 181 · Answer 10 · 2026-04-13 18:20:33

181

Views

Is the composition of an $L^2$-function with a smooth one again an $L^2$-function?

Published on 13 Apr 2026 - 18:20

score 430 · Answer 11 · 2026-05-10 19:13:08

430

Views

Proof Check: Unique Continuation of Analytic Functions

Published on 10 May 2026 - 19:13

score 533 · Answer 12 · 2026-04-17 13:01:19

533

Views

Let $G,H$ be groups and $\varphi:G \times H\to G$ and $H'=\ker(\varphi)$. Show that $(G\times H)/H'\cong G$

Published on 17 Apr 2026 - 13:01

score 39 · Answer 13 · 2026-04-16 09:33:10

39

Views

Does $\int^{\infty}_{0}pa^{p-1}1_{\{|f|>a\}}(x)da=\int^{|f(x)|}_{0}pa^{p-1}da$?

Published on 16 Apr 2026 - 9:33

score 1.1k · Answer 14 · 2026-04-14 18:20:59

1.1k

Views

Proving continuity and boundedness of the Fourier Transform

Published on 14 Apr 2026 - 18:20

score 155 · Answer 15 · 2026-04-12 20:21:52

155

Views

General Solution for $u(r,\theta, t)$

Published on 12 Apr 2026 - 20:21

List Question

Proving $\forall x \in \Bbb R$ and $ \epsilon \gt 0$, $N(x;\epsilon) \backslash \{x\}$ is open.

$f$ is a primitive polynomial in $Z[x]$. Show that the intersection of $fQ[x]$ with $Z[x]$ is $fZ[x]$.

What's wrong with the following proof that any interval $(a,b) \subset \mathbb{R}$ is connected?

Equivalent norms and subsets of open balls PROOF

Convolution of $L^{1}$ functions is well-defined

In showing that if $V=X \oplus Y$, then $X \cap Y = \{0\}$, is writing $v=0+v$ and $v=v+0$ for $v \in X \cap Y$ sufficient?

Let $N$ be a subgroup of a finite group $G$. Show that $|G| = |N| \cdot |G/N|$

Let $(G,\odot)$ be a finite group with identity element $e$. Show that for each $g \in G$, there is $k \in \Bbb N^+$ such that $g^k= e$

$A\times B \cong B\times A$ in a category $\mathbb{C}$

Is the composition of an $L^2$-function with a smooth one again an $L^2$-function?

Proof Check: Unique Continuation of Analytic Functions

Let $G,H$ be groups and $\varphi:G \times H\to G$ and $H'=\ker(\varphi)$. Show that $(G\times H)/H'\cong G$

Does $\int^{\infty}_{0}pa^{p-1}1_{\{|f|>a\}}(x)da=\int^{|f(x)|}_{0}pa^{p-1}da$?

Proving continuity and boundedness of the Fourier Transform

General Solution for $u(r,\theta, t)$

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