Question

Criterion for a splitting field of a quadratic polynomial to be a Galois Extension

score 34 · Answer 1 · 2026-04-14 13:06:10

34

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Criterion for a splitting field of a quadratic polynomial to be a Galois Extension

Published on 14 Apr 2026 - 13:06

score 82 · Answer 2 · 2026-04-12 04:40:48

82

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Proving a theorem in Galois Theory in a strange manner. Is the following proof valid?

Published on 12 Apr 2026 - 4:40

score 175 · Answer 3 · 2026-04-16 08:42:08

175

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Category theory: ex. 3.3.vi from Riehl's "Category Theory in Context"

Published on 16 Apr 2026 - 8:42

score 202 · Answer 4 · 2026-04-14 15:14:10

202

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The dual basis spans the vector space of linear transformations.

Published on 14 Apr 2026 - 15:14

score 66 · Answer 5 · 2026-04-15 16:27:27

66

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Prove that a particular sequence $l_n$ representing the amount of natural numbers $p$ satisfying $100n + 1 \le p^2 \le 100(n+1)$ is divergent

Published on 15 Apr 2026 - 16:27

score 754 · Answer 6 · 2026-04-14 21:31:25

754

Views

If $m$ and $n$ are odd positive integers, then $n^2+m^2$ is not a perfect square.

Published on 14 Apr 2026 - 21:31

score 274 · Answer 7 · 2026-04-16 02:32:14

274

Views

Proof verification that if $y_n = \sum_{k=1}^n x_n$ converges then $\lim_{n\to\infty} x_n = 0$

Published on 16 Apr 2026 - 2:32

score 333 · Answer 8 · 2026-04-11 21:32:22

333

Views

Proving $f$ is continuous iff all the functions parameterized are continuous

Published on 11 Apr 2026 - 21:32

score 283 · Answer 9 · 2026-04-28 17:47:28

283

Views

$\sigma$-fields can not be countably infinite

Published on 28 Apr 2026 - 17:47

score 338 · Answer 10 · 2026-04-28 17:51:32

338

Views

Proving the Product of topological spaces are metrizable

Published on 28 Apr 2026 - 17:51

score 134 · Answer 11 · 2026-04-15 16:20:14

134

Views

Proof verification. $\{x_n\}$ is a sequence such that $|x_{n+1} - x_n| \le C\alpha^n$ for $\alpha\in (0, 1), n\in\Bbb N$. Prove $x_n$ converges.

Published on 15 Apr 2026 - 16:20

score 234 · Answer 12 · 2026-04-13 20:58:09

234

Views

Any subcollection $\mathcal A_1$ of a locally finite collection $\mathcal A$ of subsets of $X$ is locally finite.

Published on 13 Apr 2026 - 20:58

score 63 · Answer 13 · 2026-04-14 11:04:41

63

Views

Collection $\mathcal B=${$\bar A:A\in \mathcal A$} is locally finite,given that $\mathcal A$ is locally finite.

Published on 14 Apr 2026 - 11:04

score 265 · Answer 14 · 2026-04-13 23:41:28

265

Views

How can I prove that $\frac{e^x+e^y}{2}>e^\frac{x+y}{2}$, where $x \neq y$?

Published on 13 Apr 2026 - 23:41

score 735 · Answer 15 · 2026-04-11 12:40:41

735

Views

Proving every compact space is locally compact.

Published on 11 Apr 2026 - 12:40

List Question

Criterion for a splitting field of a quadratic polynomial to be a Galois Extension

Proving a theorem in Galois Theory in a strange manner. Is the following proof valid?

Category theory: ex. 3.3.vi from Riehl's "Category Theory in Context"

The dual basis spans the vector space of linear transformations.

Prove that a particular sequence $l_n$ representing the amount of natural numbers $p$ satisfying $100n + 1 \le p^2 \le 100(n+1)$ is divergent

If $m$ and $n$ are odd positive integers, then $n^2+m^2$ is not a perfect square.

Proof verification that if $y_n = \sum_{k=1}^n x_n$ converges then $\lim_{n\to\infty} x_n = 0$

Proving $f$ is continuous iff all the functions parameterized are continuous

$\sigma$-fields can not be countably infinite

Proving the Product of topological spaces are metrizable

Proof verification. $\{x_n\}$ is a sequence such that $|x_{n+1} - x_n| \le C\alpha^n$ for $\alpha\in (0, 1), n\in\Bbb N$. Prove $x_n$ converges.

Any subcollection $\mathcal A_1$ of a locally finite collection $\mathcal A$ of subsets of $X$ is locally finite.

Collection $\mathcal B=${$\bar A:A\in \mathcal A$} is locally finite,given that $\mathcal A$ is locally finite.

How can I prove that $\frac{e^x+e^y}{2}>e^\frac{x+y}{2}$, where $x \neq y$?

Proving every compact space is locally compact.

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