Question

Is "every non-empty set is injective" equivalent to AC?

score 103 · Answer 1 · 2018-08-18 08:11:06

103

Views

Is "every non-empty set is injective" equivalent to AC?

Published on 18 Aug 2018 - 8:11

score 228 · Answer 2 · 2026-03-26 00:53:43

228

Views

Does this construction of total order use axiom of choice?

Published on 26 Mar 2026 - 0:53

score 274 · Answer 3 · 2026-03-25 12:12:25

274

Views

Choice and the principle of transfinite induction

Published on 25 Mar 2026 - 12:12

score 1k · Answer 4 · 2026-03-22 13:26:38

1k

Views

How to formally use transfinite recursion to construct a sequence for a proof of Zorn's lemma

Published on 22 Mar 2026 - 13:26

score 510 · Answer 5 · 2018-08-27 08:10:39

510

Views

Can all sets be totally ordered (not well-ordered) in ZF?

Published on 27 Aug 2018 - 8:10

score 421 · Answer 6 · 2018-08-30 13:03:33

421

Views

Why the fact that surjective map has an inverse at right is equivalent to axiom of choice?

Published on 30 Aug 2018 - 13:03

score 64 · Answer 7 · 2018-08-30 17:00:42

64

Views

Why it is necessary to state axiom of choice for a collection of sets instead of for one set?

Published on 30 Aug 2018 - 17:00

score 85 · Answer 8 · 2018-09-01 12:20:57

85

Views

Do we need Axiom of Choice to prove $|\prod_{i\in J}A_i| \le |\prod_{i\in I}A_i|$ for all $J \subseteq I$ where $I \setminus J$ is infinite?

Published on 01 Sep 2018 - 12:20

score 1.1k · Answer 9 · 2018-09-04 09:10:21

1.1k

Views

Why is this not a choice function from subsets of $\Bbb R$?

Published on 04 Sep 2018 - 9:10

score 183 · Answer 10 · 2018-09-06 11:13:49

183

Views

Role of Equality Axiom in Russell Sock Axiom Of Choice Example

Published on 06 Sep 2018 - 11:13

score 206 · Answer 11 · 2026-03-25 16:46:25

206

Views

Who was the first to mention that the well-ordering theorem implies the axiom of choice?

Published on 25 Mar 2026 - 16:46

score 40 · Answer 12 · 2018-09-08 09:10:10

40

Views

What's wrong with my argument of choice function from infinite family of nonempty sets?

Published on 08 Sep 2018 - 9:10

score 268 · Answer 13 · 2018-09-08 16:34:07

268

Views

Do I use the axiom of choice when I construct a sequence that converge?

Published on 08 Sep 2018 - 16:34

score 308 · Answer 14 · 2018-09-09 03:24:33

308

Views

Without Axiom of Choice, Is there anything wrong with my proof that $\aleph_0$ is the smallest cardinality of infinite sets?

Published on 09 Sep 2018 - 3:24

score 65 · Answer 15 · 2018-09-12 16:05:06

65

Views

Absent choice, if $A$ and $B$ have a bijection, must every surjective function from $A$ to $B$ have a right inverse?

Published on 12 Sep 2018 - 16:05

List Question

Is "every non-empty set is injective" equivalent to AC?

Does this construction of total order use axiom of choice?

Choice and the principle of transfinite induction

How to formally use transfinite recursion to construct a sequence for a proof of Zorn's lemma

Can all sets be totally ordered (not well-ordered) in ZF?

Why the fact that surjective map has an inverse at right is equivalent to axiom of choice?

Why it is necessary to state axiom of choice for a collection of sets instead of for one set?

Do we need Axiom of Choice to prove $|\prod_{i\in J}A_i| \le |\prod_{i\in I}A_i|$ for all $J \subseteq I$ where $I \setminus J$ is infinite?

Why is this not a choice function from subsets of $\Bbb R$?

Role of Equality Axiom in Russell Sock Axiom Of Choice Example

Who was the first to mention that the well-ordering theorem implies the axiom of choice?

What's wrong with my argument of choice function from infinite family of nonempty sets?

Do I use the axiom of choice when I construct a sequence that converge?

Without Axiom of Choice, Is there anything wrong with my proof that $\aleph_0$ is the smallest cardinality of infinite sets?

Absent choice, if $A$ and $B$ have a bijection, must every surjective function from $A$ to $B$ have a right inverse?

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