Question

Do an infinite set and its double have the same cardinality?

score 118 · Answer 1 · 2026-04-02 12:23:17

118

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Do an infinite set and its double have the same cardinality?

Published on 02 Apr 2026 - 12:23

score 308 · Answer 2 · 2015-01-08 22:59:01

308

Views

Prove that $2^\aleph+\aleph$ equals $2^\aleph$.

Published on 08 Jan 2015 - 22:59

score 71 · Answer 3 · 2015-01-09 10:04:26

71

Views

Prove $α · β ≤ α · γ$ and $α^ β ≤ α^ γ$ for any three cardinals, where $ β ≤ γ$.

Published on 09 Jan 2015 - 10:04

score 102 · Answer 4 · 2015-01-09 12:39:15

102

Views

Prove that if A~B then Sym(A)~Sym(B).

Published on 09 Jan 2015 - 12:39

score 91 · Answer 5 · 2015-01-10 00:04:35

91

Views

Notation about cardinals

Published on 10 Jan 2015 - 0:04

score 1.2k · Answer 6 · 2026-03-26 05:54:36

1.2k

Views

Are there fields and ordered fields of every infinite cardinality?

Published on 26 Mar 2026 - 5:54

score 192 · Answer 7 · 2015-01-11 19:40:45

192

Views

Are injections harder to find than surjections?

Published on 11 Jan 2015 - 19:40

score 119 · Answer 8 · 2015-01-12 20:38:41

119

Views

closed unbounded set,regular cardinals,cofinality

Published on 12 Jan 2015 - 20:38

score 432 · Answer 9 · 2015-01-13 21:45:34

432

Views

Is it true that $({\aleph_1})^{\aleph_0} = {\aleph_1}$?

Published on 13 Jan 2015 - 21:45

score 406 · Answer 10 · 2015-01-14 07:09:24

406

Views

Cofinality of $2^{\aleph_\omega}$

Published on 14 Jan 2015 - 7:09

score 91 · Answer 11 · 2015-01-17 08:56:31

If $\alpha$, $\beta$ are finite cardinals such that both are greater than $1$ and $\gamma$ is an infinite cardinal then $\alpha^\gamma=\beta^\gamma$.

score 96 · Answer 12 · 2015-01-17 09:32:47

96

Views

I can't find the mistake in this argument (Cofinality and König's theorem)

Published on 17 Jan 2015 - 9:32

score 142 · Answer 13 · 2015-01-17 11:22:17

142

Views

$\aleph_0 \aleph_1 =\aleph_1$? But I don’t know any way to prove or disprove it

Published on 17 Jan 2015 - 11:22

score 117 · Answer 14 · 2015-01-19 19:17:18

117

Views

Find the maximum number of a continuous function

Published on 19 Jan 2015 - 19:17

score 1.2k · Answer 15 · 2015-01-20 12:17:17

1.2k

Views

what is the cardinality of powerset of a union set?

Published on 20 Jan 2015 - 12:17

List Question

Do an infinite set and its double have the same cardinality?

Prove that $2^\aleph+\aleph$ equals $2^\aleph$.

Prove $α · β ≤ α · γ$ and $α^ β ≤ α^ γ$ for any three cardinals, where $ β ≤ γ$.

Prove that if A~B then Sym(A)~Sym(B).

Notation about cardinals

Are there fields and ordered fields of every infinite cardinality?

Are injections harder to find than surjections?

closed unbounded set,regular cardinals,cofinality

Is it true that $({\aleph_1})^{\aleph_0} = {\aleph_1}$?

Cofinality of $2^{\aleph_\omega}$

If $\alpha$, $\beta$ are finite cardinals such that both are greater than $1$ and $\gamma$ is an infinite cardinal then $\alpha^\gamma=\beta^\gamma$.

I can't find the mistake in this argument (Cofinality and König's theorem)

$\aleph_0 \aleph_1 =\aleph_1$? But I don’t know any way to prove or disprove it

Find the maximum number of a continuous function

what is the cardinality of powerset of a union set?

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