Question

Cardinality of cartesian square

score 5.6k · Answer 1 · 2012-08-09 13:35:27

5.6k

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Cardinality of cartesian square

Published on 09 Aug 2012 - 13:35

score 1.4k · Answer 2 · 2026-04-06 22:01:57

1.4k

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Is cardinality a total order? Is AC necessary?

Published on 06 Apr 2026 - 22:01

score 300 · Answer 3 · 2026-04-06 22:02:10

300

Views

Sum of cardinals without AC

Published on 06 Apr 2026 - 22:02

score 203 · Answer 4 · 2026-04-08 06:11:06

203

Views

Rational numbers and cardinality of some subset set of them.

Published on 08 Apr 2026 - 6:11

score 397 · Answer 5 · 2012-08-13 00:33:23

397

Views

Cardinal exponentiation problem from Halmos' Naive Set Theory

Published on 13 Aug 2012 - 0:33

score 386 · Answer 6 · 2026-03-29 13:50:01

386

Views

When collapsing a cardinal, what ordinal does it become?

Published on 29 Mar 2026 - 13:50

score 18.6k · Answer 7 · 2026-04-07 14:40:23

18.6k

Views

Why do the rationals, integers and naturals all have the same cardinality?

Published on 07 Apr 2026 - 14:40

score 3.7k · Answer 8 · 2026-04-09 10:10:51

3.7k

Views

How do you prove the trichotomy law for cardinal numbers?

Published on 09 Apr 2026 - 10:10

score 212 · Answer 9 · 2012-08-15 19:00:11

212

Views

Proving $|A^A|=|2^A|$ for infinite $A$.

Published on 15 Aug 2012 - 19:00

score 2.3k · Answer 10 · 2026-04-09 08:17:10

2.3k

Views

What is $\aleph_0$ powered to $\aleph_0$?

Published on 09 Apr 2026 - 8:17

score 103 · Answer 11 · 2012-08-18 20:17:19

103

Views

If $a, p$ are cardinals satisfying $2 p = p$ and $a+p=2^p,$ then $a \ge 2^p.$

Published on 18 Aug 2012 - 20:17

score 1.6k · Answer 12 · 2012-08-20 19:08:11

1.6k

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The cardinality of the set of countably infinite subsets of an infinite set

Published on 20 Aug 2012 - 19:08

score 1k · Answer 13 · 2026-04-05 01:48:32

1k

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How does the supremum of the cardinalities of a set of ordinals relate to the supremum of the ordinals?

Published on 05 Apr 2026 - 1:48

score 260 · Answer 14 · 2012-08-23 16:50:58

260

Views

Closing a subcategory under finite colimits by transfinite induction

Published on 23 Aug 2012 - 16:50

score 617 · Answer 15 · 2026-04-05 01:47:45

617

Views

If $\kappa$ is a cardinal, $\aleph$ is any $\aleph$-number, and if $\kappa\leq\aleph$ then $\kappa$ can be well ordered as well.

Published on 05 Apr 2026 - 1:47

List Question

Cardinality of cartesian square

Is cardinality a total order? Is AC necessary?

Sum of cardinals without AC

Rational numbers and cardinality of some subset set of them.

Cardinal exponentiation problem from Halmos' Naive Set Theory

When collapsing a cardinal, what ordinal does it become?

Why do the rationals, integers and naturals all have the same cardinality?

How do you prove the trichotomy law for cardinal numbers?

Proving $|A^A|=|2^A|$ for infinite $A$.

What is $\aleph_0$ powered to $\aleph_0$?

If $a, p$ are cardinals satisfying $2 p = p$ and $a+p=2^p,$ then $a \ge 2^p.$

The cardinality of the set of countably infinite subsets of an infinite set

How does the supremum of the cardinalities of a set of ordinals relate to the supremum of the ordinals?

Closing a subcategory under finite colimits by transfinite induction

If $\kappa$ is a cardinal, $\aleph$ is any $\aleph$-number, and if $\kappa\leq\aleph$ then $\kappa$ can be well ordered as well.

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