Question

Finding a basis of an infinite dimensional vector space with a given vector

score 488 · Answer 1 · 2019-02-20 03:04:04

488

Views

Finding a basis of an infinite dimensional vector space with a given vector

Published on 20 Feb 2019 - 3:04

score 107 · Answer 2 · 2019-02-22 13:59:06

107

Views

Construction of the equivalence of the finite ordinal category and the category of finite sets

Published on 22 Feb 2019 - 13:59

score 108 · Answer 3 · 2019-02-24 05:18:25

108

Views

Any infinite set contains a countable subset. Why is my proof wrong? (Axiom of Choice)

Published on 24 Feb 2019 - 5:18

score 410 · Answer 4 · 2019-02-25 19:00:43

410

Views

Axiom of Countable Choice - Consequences

Published on 25 Feb 2019 - 19:00

score 233 · Answer 5 · 2026-03-25 13:13:23

233

Views

Usage of Zorn's Lemma to prove that the intersection of all prime ideals contains only nilpotent elements.

Published on 25 Mar 2026 - 13:13

score 228 · Answer 6 · 2026-03-26 06:34:22

228

Views

Proving (without AC) that there is a surjective function from $\mathcal{P}(\omega)$ to $\omega_1$.

Published on 26 Mar 2026 - 6:34

score 109 · Answer 7 · 2026-03-25 03:21:29

109

Views

Does the statement "Every short exact sequence of vector spaces splits" imply the axiom of choice?

Published on 25 Mar 2026 - 3:21

score 167 · Answer 8 · 2019-03-07 02:56:57

167

Views

Axiom of choice and dual of a tensor product

Published on 07 Mar 2019 - 2:56

score 287 · Answer 9 · 2026-03-25 23:34:43

287

Views

Help understanding Well-Ordering Theorem

Published on 25 Mar 2026 - 23:34

score 463 · Answer 10 · 2026-03-25 21:22:57

463

Views

How strong is the axiom of well-ordered choice?

Published on 25 Mar 2026 - 21:22

score 101 · Answer 11 · 2026-03-25 03:21:14

101

Views

Does the existence of a linear functional on $C_0^\infty(\mathbb R)$ which is not a distribution require the axiom of choice?

Published on 25 Mar 2026 - 3:21

score 343 · Answer 12 · 2026-03-25 21:31:32

343

Views

Why is the Axiom of Well-ordered Choice not strong enough to prove Zorn's Lemma?

Published on 25 Mar 2026 - 21:31

score 227 · Answer 13 · 2019-03-13 15:45:22

227

Views

Is the Axiom of Choice necessary in the proof that any subset of a metric space that contains its limit points is closed?

Published on 13 Mar 2019 - 15:45

score 190 · Answer 14 · 2026-03-26 01:03:19

190

Views

Given $S \hookrightarrow T$ construct $U ≈ T$ disjoint from $S$ in Z set theory?

Published on 26 Mar 2026 - 1:03

score 162 · Answer 15 · 2019-03-22 23:00:14

162

Views

Banach-Tarski nonparadox: Reassembling a ball into two balls with a total volume equal to the original volume

Published on 22 Mar 2019 - 23:00

List Question

Finding a basis of an infinite dimensional vector space with a given vector

Construction of the equivalence of the finite ordinal category and the category of finite sets

Any infinite set contains a countable subset. Why is my proof wrong? (Axiom of Choice)

Axiom of Countable Choice - Consequences

Usage of Zorn's Lemma to prove that the intersection of all prime ideals contains only nilpotent elements.

Proving (without AC) that there is a surjective function from $\mathcal{P}(\omega)$ to $\omega_1$.

Does the statement "Every short exact sequence of vector spaces splits" imply the axiom of choice?

Axiom of choice and dual of a tensor product

Help understanding Well-Ordering Theorem

How strong is the axiom of well-ordered choice?

Does the existence of a linear functional on $C_0^\infty(\mathbb R)$ which is not a distribution require the axiom of choice?

Why is the Axiom of Well-ordered Choice not strong enough to prove Zorn's Lemma?

Is the Axiom of Choice necessary in the proof that any subset of a metric space that contains its limit points is closed?

Given $S \hookrightarrow T$ construct $U ≈ T$ disjoint from $S$ in Z set theory?

Banach-Tarski nonparadox: Reassembling a ball into two balls with a total volume equal to the original volume

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