Question

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

score 151 · Answer 1 · 2026-05-10 16:12:42

151

Views

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

Published on 10 May 2026 - 16:12

score 344 · Answer 2 · 2026-04-26 15:08:56

344

Views

Existence of Aronszajn tree

Published on 26 Apr 2026 - 15:08

score 260 · Answer 3 · 2026-05-10 12:35:38

260

Views

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

Published on 10 May 2026 - 12:35

score 209 · Answer 4 · 2026-04-29 23:30:51

209

Views

Is this Theorem equivalent to Axiom of Choice?

Published on 29 Apr 2026 - 23:30

score 296 · Answer 5 · 2026-04-29 23:31:00

296

Views

Prove that Axiom of Dependent Choice implies Axiom of Countable Choice

Published on 29 Apr 2026 - 23:31

score 287 · Answer 6 · 2026-04-29 23:30:52

287

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 29 Apr 2026 - 23:30

score 72 · Answer 7 · 2026-04-29 23:30:49

72

Views

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

Published on 29 Apr 2026 - 23:30

score 154 · Answer 8 · 2026-04-29 23:30:51

154

Views

Inequality about infinite cardinals

Published on 29 Apr 2026 - 23:30

score 80 · Answer 9 · 2026-04-29 23:31:22

80

Views

Relation between choice principles

Published on 29 Apr 2026 - 23:31

score 80 · Answer 10 · 2026-04-29 23:30:52

80

Views

Lebesgue monotone convergence: step functions w/o choice

Published on 29 Apr 2026 - 23:30

score 2.4k · Answer 11 · 2026-05-11 08:40:57

2.4k

Views

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

Published on 11 May 2026 - 8:40

score 266 · Answer 12 · 2026-05-10 12:34:42

266

Views

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

Published on 10 May 2026 - 12:34

score 356 · Answer 13 · 2026-05-10 23:38:28

356

Views

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

Published on 10 May 2026 - 23:38

score 208 · Answer 14 · 2026-04-29 23:31:22

208

Views

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

Published on 29 Apr 2026 - 23:31

score 45 · Answer 15 · 2026-04-29 23:31:22

45

Views

Schröder–Bernstein theorem for finite sets

Published on 29 Apr 2026 - 23:31

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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