Question

$\mathbb{R}^2$ and the axiom of choice

score 146 · Answer 1 · 2026-03-25 03:07:36

146

Views

$\mathbb{R}^2$ and the axiom of choice

Published on 25 Mar 2026 - 3:07

score 334 · Answer 2 · 2026-03-25 03:58:42

334

Views

Existence of Aronszajn tree

Published on 25 Mar 2026 - 3:58

score 256 · Answer 3 · 2026-03-25 14:16:45

256

Views

Trouble finding a proof that well-ordering of the reals is independent of ZF

Published on 25 Mar 2026 - 14:16

score 205 · Answer 4 · 2026-03-22 20:05:56

205

Views

Is this Theorem equivalent to Axiom of Choice?

Published on 22 Mar 2026 - 20:05

score 291 · Answer 5 · 2018-04-24 01:20:53

291

Views

Prove that Axiom of Dependent Choice implies Axiom of Countable Choice

Published on 24 Apr 2018 - 1:20

score 283 · Answer 6 · 2018-04-25 23:58:14

283

Views

Proof for an infinite sequence of increasing sets that a set $B$ (with conditions) is a member of one of them using the axiom of choice

Published on 25 Apr 2018 - 23:58

score 68 · Answer 7 · 2018-04-26 05:41:14

68

Views

Possible mistakes in a proof of the equivalence of Axiom of Choice

Published on 26 Apr 2018 - 5:41

score 150 · Answer 8 · 2026-03-22 02:58:20

150

Views

Inequality about infinite cardinals

Published on 22 Mar 2026 - 2:58

score 75 · Answer 9 · 2026-03-22 03:49:14

75

Views

Relation between choice principles

Published on 22 Mar 2026 - 3:49

score 77 · Answer 10 · 2026-03-26 01:28:54

77

Views

Lebesgue monotone convergence: step functions w/o choice

Published on 26 Mar 2026 - 1:28

score 2.4k · Answer 11 · 2026-03-25 10:59:04

2.4k

Views

Is there a simple example of how the axiom of choice can lead to a counterintuitive result?

Published on 25 Mar 2026 - 10:59

score 258 · Answer 12 · 2026-03-25 10:57:30

258

Views

Are any of the counterintuitive functions whose existence is postulated by the axiom of choice computable?

Published on 25 Mar 2026 - 10:57

score 350 · Answer 13 · 2026-03-25 20:36:06

350

Views

How does the Axiom of Choice affect the ability to determine that $|\mathcal{P}(\omega)|$ is an uncountable cardinal

Published on 25 Mar 2026 - 20:36

score 201 · Answer 14 · 2018-05-16 11:11:39

201

Views

Non-degeneracy of pairing between vector space and its dual - but without Choice

Published on 16 May 2018 - 11:11

score 40 · Answer 15 · 2018-05-18 12:47:38

40

Views

Schröder–Bernstein theorem for finite sets

Published on 18 May 2018 - 12:47

List Question

$\mathbb{R}^2$ and the axiom of choice

Existence of Aronszajn tree

Trouble finding a proof that well-ordering of the reals is independent of ZF

Is this Theorem equivalent to Axiom of Choice?

Prove that Axiom of Dependent Choice implies Axiom of Countable Choice

Proof for an infinite sequence of increasing sets that a set $B$ (with conditions) is a member of one of them using the axiom of choice

Possible mistakes in a proof of the equivalence of Axiom of Choice

Inequality about infinite cardinals

Relation between choice principles

Lebesgue monotone convergence: step functions w/o choice

Is there a simple example of how the axiom of choice can lead to a counterintuitive result?

Are any of the counterintuitive functions whose existence is postulated by the axiom of choice computable?

How does the Axiom of Choice affect the ability to determine that $|\mathcal{P}(\omega)|$ is an uncountable cardinal

Non-degeneracy of pairing between vector space and its dual - but without Choice

Schröder–Bernstein theorem for finite sets

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