Question

Should axioms be seen as "building blocks of definitions"?

score 362 · Answer 1 · 2026-03-19 19:34:56

362

Views

Should axioms be seen as "building blocks of definitions"?

Published on 19 Mar 2026 - 19:34

score 658 · Answer 2 · 2026-03-22 13:34:20

658

Views

Non-standard axioms + ZF and rest of math

Published on 22 Mar 2026 - 13:34

score 161 · Answer 3 · 2026-03-22 14:19:35

161

Views

Does $\mathbb{R}$ have any axioms?

Published on 22 Mar 2026 - 14:19

score 122 · Answer 4 · 2026-03-20 06:06:34

122

Views

Finite axiomatizability of theories in infinitary logic?

Published on 20 Mar 2026 - 6:06

score 257 · Answer 5 · 2026-03-23 09:30:29

257

Views

Continuity axioms and completness axioms for real numbers are the same things?

Published on 23 Mar 2026 - 9:30

score 591 · Answer 6 · 2026-03-21 09:27:48

591

Views

Why don't we have many non euclidean geometries out there?

Published on 21 Mar 2026 - 9:27

score 1.4k · Answer 7 · 2026-03-20 06:22:02

1.4k

Views

Why do we need the axiom of choice?

Published on 20 Mar 2026 - 6:22

score 2.5k · Answer 8 · 2026-03-20 11:35:58

2.5k

Views

What axioms Gödel is using, if any?

Published on 20 Mar 2026 - 11:35

score 47 · Answer 9 · 2026-03-20 19:21:19

47

Views

Determine if U a subspace of $P_3$?

Published on 20 Mar 2026 - 19:21

score 490 · Answer 10 · 2026-03-21 07:44:03

490

Views

Why such stark contrast between the approach to the continuum hypothesis in set theory and the approach to the parallel postulate in geometry?

Published on 21 Mar 2026 - 7:44

score 154 · Answer 11 · 2026-03-21 05:17:34

154

Views

Prove inequality using Positivity Axioms

Published on 21 Mar 2026 - 5:17

score 2.3k · Answer 12 · 2026-03-20 01:32:04

Consider an experiment whose sample space consists of a countably infinite number of outcomes. Show that not all outcomes can be equally likely.

score 273 · Answer 13 · 2026-03-22 08:40:11

273

Views

What means "equal" in Euclid 4th postulate?

Published on 22 Mar 2026 - 8:40

score 145 · Answer 14 · 2026-03-24 02:23:14

145

Views

Is it possible to construct a formal system such that all interesting statements from ZFC can be proven within the system?

Published on 24 Mar 2026 - 2:23

score 101 · Answer 15 · 2026-03-20 10:34:56

101

Views

Why is this axiom written twice?

Published on 20 Mar 2026 - 10:34

List Question

Should axioms be seen as "building blocks of definitions"?

Non-standard axioms + ZF and rest of math

Does $\mathbb{R}$ have any axioms?

Finite axiomatizability of theories in infinitary logic?

Continuity axioms and completness axioms for real numbers are the same things?

Why don't we have many non euclidean geometries out there?

Why do we need the axiom of choice?

What axioms Gödel is using, if any?

Determine if U a subspace of $P_3$?

Why such stark contrast between the approach to the continuum hypothesis in set theory and the approach to the parallel postulate in geometry?

Prove inequality using Positivity Axioms

Consider an experiment whose sample space consists of a countably infinite number of outcomes. Show that not all outcomes can be equally likely.

What means "equal" in Euclid 4th postulate?

Is it possible to construct a formal system such that all interesting statements from ZFC can be proven within the system?

Why is this axiom written twice?

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