Question

About the proof that an infinite ordinal has the same cardinality as its successor

score 766 · Answer 1 · 2026-04-13 19:59:02

766

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About the proof that an infinite ordinal has the same cardinality as its successor

Published on 13 Apr 2026 - 19:59

score 666 · Answer 2 · 2026-04-13 13:42:19

666

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Why do we define ordinals the way we do?

Published on 13 Apr 2026 - 13:42

score 68 · Answer 3 · 2026-04-13 16:56:15

68

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Prove that $b\cdot\aleph_0=b$, where b is an infinite set.

Published on 13 Apr 2026 - 16:56

score 999 · Answer 4 · 2026-04-14 23:15:15

999

Views

Cambridge Tripos 2015: Zorn's Lemma Proof Requiring Axiom of Choice

Published on 14 Apr 2026 - 23:15

score 150 · Answer 5 · 2026-04-11 05:11:25

150

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Why such $\theta$ exists by replacement?

Published on 11 Apr 2026 - 5:11

score 452 · Answer 6 · 2026-04-16 04:21:26

452

Views

Small and large categories when category theory is taken as the foundation of mathematics

Published on 16 Apr 2026 - 4:21

score 180 · Answer 7 · 2026-04-09 01:31:03

180

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Infinite family $\mathscr{A}\subseteq P(\omega)$ with criteria

Published on 09 Apr 2026 - 1:31

score 111 · Answer 8 · 2026-04-16 02:43:30

111

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Interdefinability of set, type and category theories

Published on 16 Apr 2026 - 2:43

score 212 · Answer 9 · 2026-04-12 02:27:58

212

Views

The recursion theorem - approach

Published on 12 Apr 2026 - 2:27

score 316 · Answer 10 · 2026-04-14 06:28:37

316

Views

Proof: $\kappa \cdot \kappa = \kappa$ for infinite cardinals

Published on 14 Apr 2026 - 6:28

score 233 · Answer 11 · 2026-04-16 23:30:48

233

Views

Find ordinal numbers $a$, $b$ and $c$ so that $(a\cdot b)^c$ is not equal to $a^c \cdot b^c$

Published on 16 Apr 2026 - 23:30

score 752 · Answer 12 · 2026-04-15 20:46:30

752

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Set theory ordinals problem Prove that if $b$ is a limit ordinal and $a<b$ then $a+b=b$ (a is any ordinal number)

Published on 15 Apr 2026 - 20:46

score 189 · Answer 13 · 2026-04-08 17:12:58

189

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Can a $\Delta_0$ formula $\varphi$ not be independent of ZFC?

Published on 08 Apr 2026 - 17:12

score 422 · Answer 14 · 2026-04-11 17:51:17

422

Views

Is there a reason Halmos defined continuation on well-ordered sets, but not total ordered sets?

Published on 11 Apr 2026 - 17:51

score 271 · Answer 15 · 2026-04-11 20:22:27

271

Views

Equivalence of Dedekind infinity and infinity, and Axiom of Choice

Published on 11 Apr 2026 - 20:22

List Question

About the proof that an infinite ordinal has the same cardinality as its successor

Why do we define ordinals the way we do?

Prove that $b\cdot\aleph_0=b$, where b is an infinite set.

Cambridge Tripos 2015: Zorn's Lemma Proof Requiring Axiom of Choice

Why such $\theta$ exists by replacement?

Small and large categories when category theory is taken as the foundation of mathematics

Infinite family $\mathscr{A}\subseteq P(\omega)$ with criteria

Interdefinability of set, type and category theories

The recursion theorem - approach

Proof: $\kappa \cdot \kappa = \kappa$ for infinite cardinals

Find ordinal numbers $a$, $b$ and $c$ so that $(a\cdot b)^c$ is not equal to $a^c \cdot b^c$

Set theory ordinals problem Prove that if $b$ is a limit ordinal and $a<b$ then $a+b=b$ (a is any ordinal number)

Can a $\Delta_0$ formula $\varphi$ not be independent of ZFC?

Is there a reason Halmos defined continuation on well-ordered sets, but not total ordered sets?

Equivalence of Dedekind infinity and infinity, and Axiom of Choice

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