Question

How can I describe the set of homomorphisms and what is its cardinality?

score 477 · Answer 1 · 2026-03-25 15:42:21

477

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How can I describe the set of homomorphisms and what is its cardinality?

Published on 25 Mar 2026 - 15:42

score 526 · Answer 2 · 2019-07-12 23:56:17

526

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Proof Verification that Every Finite Set has a Unique Cardinality

Published on 12 Jul 2019 - 23:56

score 1.6k · Answer 3 · 2019-07-13 00:55:13

1.6k

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A Set is Infinite if, and only if, it is in One-to-one Correspondence with a Proper Subset of Itself

Published on 13 Jul 2019 - 0:55

score 128 · Answer 4 · 2019-07-14 03:48:24

128

Views

If $X$ is an infinite set, then is $\sum_{i=1}^\infty |X|=|X|$?

Published on 14 Jul 2019 - 3:48

score 53 · Answer 5 · 2019-07-15 07:55:00

53

Views

Does $|A|^{|A|}=2^{|A|}$ hold for any infinite set $A$?

Published on 15 Jul 2019 - 7:55

score 121 · Answer 6 · 2026-03-25 15:58:43

121

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On the distributive number $\mathfrak h$

Published on 25 Mar 2026 - 15:58

score 109 · Answer 7 · 2026-03-25 20:12:49

109

Views

Infinite Time Turing Machine and Hypertask

Published on 25 Mar 2026 - 20:12

score 544 · Answer 8 · 2019-07-18 14:30:51

544

Views

Prove that for any set A and B, the cardinality of the set of all functions mapping A to B is $\vert B \vert ^ {\vert A \vert}$

Published on 18 Jul 2019 - 14:30

score 89 · Answer 9 · 2019-07-19 00:34:02

Prove that for any set A, if $\vert \Bbb N \times \Bbb R \vert \geqslant \vert A \vert$, then $\vert \Bbb R \vert \geqslant \vert A \vert$.

score 650 · Answer 10 · 2019-07-19 22:03:44

650

Views

Let $S$ be the set of all possible functions mapping $\{\sqrt 2, \sqrt 3, \sqrt 5, \sqrt 7 \}$ to $\Bbb Q$, find the cardinality of $S$.

Published on 19 Jul 2019 - 22:03

score 152 · Answer 11 · 2026-03-26 17:52:52

152

Views

Example of non well-orderable set in ZF.

Published on 26 Mar 2026 - 17:52

score 140 · Answer 12 · 2026-03-26 17:53:27

140

Views

Show that the cardinality of ($X$ ∪ {$x$}) is equal to the cardianlity of ($X$)+$1$

Published on 26 Mar 2026 - 17:53

score 412 · Answer 13 · 2019-07-22 19:57:20

412

Views

What is the cardinality of $L^{\infty}(\mathbb{R})$?

Published on 22 Jul 2019 - 19:57

score 153 · Answer 14 · 2019-07-23 13:19:19

153

Views

Cardinality of the continuum and binary expansion of numbers

Published on 23 Jul 2019 - 13:19

score 63 · Answer 15 · 2019-07-25 00:51:07

63

Views

Is there a cardinal function such that the intersection of a family of open sets with the same cardinality has an open intersection?

Published on 25 Jul 2019 - 0:51

List Question

How can I describe the set of homomorphisms and what is its cardinality?

Proof Verification that Every Finite Set has a Unique Cardinality

A Set is Infinite if, and only if, it is in One-to-one Correspondence with a Proper Subset of Itself

If $X$ is an infinite set, then is $\sum_{i=1}^\infty |X|=|X|$?

Does $|A|^{|A|}=2^{|A|}$ hold for any infinite set $A$?

On the distributive number $\mathfrak h$

Infinite Time Turing Machine and Hypertask

Prove that for any set A and B, the cardinality of the set of all functions mapping A to B is $\vert B \vert ^ {\vert A \vert}$

Prove that for any set A, if $\vert \Bbb N \times \Bbb R \vert \geqslant \vert A \vert$, then $\vert \Bbb R \vert \geqslant \vert A \vert$.

Let $S$ be the set of all possible functions mapping $\{\sqrt 2, \sqrt 3, \sqrt 5, \sqrt 7 \}$ to $\Bbb Q$, find the cardinality of $S$.

Example of non well-orderable set in ZF.

Show that the cardinality of ($X$ ∪ {$x$}) is equal to the cardianlity of ($X$)+$1$

What is the cardinality of $L^{\infty}(\mathbb{R})$?

Cardinality of the continuum and binary expansion of numbers

Is there a cardinal function such that the intersection of a family of open sets with the same cardinality has an open intersection?

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