Question

Proving closed interval [0,1] has same cardinality as Real Numbers

score 56 · Answer 1 · 2018-11-02 15:39:48

56

Views

Proving closed interval [0,1] has same cardinality as Real Numbers

Published on 02 Nov 2018 - 15:39

score 237 · Answer 2 · 2018-11-02 21:07:56

237

Views

Cardinality of the set of all even functions $f : \mathbb{R} \rightarrow \mathbb{R} $

Published on 02 Nov 2018 - 21:07

score 80 · Answer 3 · 2018-11-05 12:43:48

80

Views

Is this proof of the Cantor–Bernstein theorem I wrote valid? Or did I make a mistake somewhere?

Published on 05 Nov 2018 - 12:43

score 221 · Answer 4 · 2018-11-06 18:45:15

221

Views

Finding a bijection between set of infinite sequences of $0,1,2$ and the open interval $(0,1)$

Published on 06 Nov 2018 - 18:45

score 2.2k · Answer 5 · 2018-11-07 19:09:14

2.2k

Views

Bijective map between two finite sets is equivalent to the same cardinality

Published on 07 Nov 2018 - 19:09

score 149 · Answer 6 · 2018-11-08 03:30:59

149

Views

Proof that Separable Banach Spaces are Homeomorphic and Continuum Hypothesis

Published on 08 Nov 2018 - 3:30

score 283 · Answer 7 · 2018-11-08 07:03:29

Without the Axiom of Choice, is there a bijection between $\mathcal{P}(\aleph_\alpha)$ and $\mathcal{P}(\aleph_\alpha \times \aleph_\alpha)$?

score 279 · Answer 8 · 2018-11-12 16:54:49

279

Views

Distinct Uncountable Dense Subsets of R

Published on 12 Nov 2018 - 16:54

score 452 · Answer 9 · 2018-11-12 21:54:45

452

Views

A first-countable, separable Hausdorff space has at most the continuum cardinality $c$

Published on 12 Nov 2018 - 21:54

score 33 · Answer 10 · 2018-11-13 14:37:03

33

Views

If $X$ is $T_1$, any point of $X $is $G_{\delta}$ and any discrete subset is enumerable then $|X| \leq c$

Published on 13 Nov 2018 - 14:37

score 82 · Answer 11 · 2018-11-13 20:20:54

82

Views

Prove that if $A$ is infinite and $B$ is countable, then $|A + B| = |A|$ (assume AC)

Published on 13 Nov 2018 - 20:20

score 451 · Answer 12 · 2018-11-15 07:53:50

451

Views

How many ultrafilters there are in an infinite space?

Published on 15 Nov 2018 - 7:53

score 56 · Answer 13 · 2018-11-15 09:15:23

56

Views

Suppose $\kappa$ is a cardinal, such that $2 \kappa = \kappa$. Can it be proven that $\kappa ! = 2^\kappa$ without choice?

Published on 15 Nov 2018 - 9:15

score 165 · Answer 14 · 2026-03-26 01:34:54

165

Views

Burali-Forti paradox for cardinals

Published on 26 Mar 2026 - 1:34

score 732 · Answer 15 · 2018-11-17 21:34:55

732

Views

Equivalent finite sets have the same number of elements (odd proof)

Published on 17 Nov 2018 - 21:34

List Question

Proving closed interval [0,1] has same cardinality as Real Numbers

Cardinality of the set of all even functions $f : \mathbb{R} \rightarrow \mathbb{R} $

Is this proof of the Cantor–Bernstein theorem I wrote valid? Or did I make a mistake somewhere?

Finding a bijection between set of infinite sequences of $0,1,2$ and the open interval $(0,1)$

Bijective map between two finite sets is equivalent to the same cardinality

Proof that Separable Banach Spaces are Homeomorphic and Continuum Hypothesis

Without the Axiom of Choice, is there a bijection between $\mathcal{P}(\aleph_\alpha)$ and $\mathcal{P}(\aleph_\alpha \times \aleph_\alpha)$?

Distinct Uncountable Dense Subsets of R

A first-countable, separable Hausdorff space has at most the continuum cardinality $c$

If $X$ is $T_1$, any point of $X $is $G_{\delta}$ and any discrete subset is enumerable then $|X| \leq c$

Prove that if $A$ is infinite and $B$ is countable, then $|A + B| = |A|$ (assume AC)

How many ultrafilters there are in an infinite space?

Suppose $\kappa$ is a cardinal, such that $2 \kappa = \kappa$. Can it be proven that $\kappa ! = 2^\kappa$ without choice?

Burali-Forti paradox for cardinals

Equivalent finite sets have the same number of elements (odd proof)

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