Question

Cardinality of $\{0,1\}^\mathbb{N}$

score 148 · Answer 1 · 2018-10-10 10:20:38

148

Views

Cardinality of $\{0,1\}^\mathbb{N}$

Published on 10 Oct 2018 - 10:20

score 63 · Answer 2 · 2018-10-11 02:28:16

63

Views

The set of sequences of $\Bbb N$ and $\mathcal{P} (\Bbb N)$ are equinumerous.

Published on 11 Oct 2018 - 2:28

score 343 · Answer 3 · 2018-10-11 15:15:25

343

Views

Let $X,Y,Z$ be nonempty sets. Then $|(X^Y)^Z|=|X^{Y\times Z}|$

Published on 11 Oct 2018 - 15:15

score 149 · Answer 4 · 2018-10-13 01:12:03

149

Views

Question about Hungerford's definition about cardinality

Published on 13 Oct 2018 - 1:12

score 90 · Answer 5 · 2018-10-13 16:19:15

Suppose that $\aleph_0\le |A|<|B|$. Compare $|\mathcal {P}(A)|$ and $|\mathcal {P}(B)|$, $|A^B|$ and $|B^A|$, $|B^A|$ and $|B|$

score 47 · Answer 6 · 2018-10-14 01:37:16

47

Views

Let $\mathfrak F$ be the set of injective mappings $f:\Bbb N\to\Bbb N$. Then $|\mathfrak F|=2^{\aleph_0}$

Published on 14 Oct 2018 - 1:37

score 111 · Answer 7 · 2026-03-25 20:34:03

111

Views

Injection from cardinal $\lambda$ to cardinal $\kappa$ implies $\lambda\leq\kappa$

Published on 25 Mar 2026 - 20:34

score 219 · Answer 8 · 2018-10-16 04:13:32

219

Views

Proving $A\subset B\implies |A|\leq |B|$

Published on 16 Oct 2018 - 4:13

score 91 · Answer 9 · 2026-03-25 01:20:34

91

Views

Examples of Commutative Semigroups Where the Cardinality of the Carrier Set is Greater Than $\mathfrak c$.

Published on 25 Mar 2026 - 1:20

score 676 · Answer 10 · 2018-10-21 19:09:03

676

Views

Question on injective-surjective functions, regarding cardinality of domain, codomain

Published on 21 Oct 2018 - 19:09

score 342 · Answer 11 · 2018-10-24 14:00:01

342

Views

Is $X=\left\{(x_n)_{n\in\mathbb{N}}\mid x_n\in\{0,1\},\forall n \wedge x_n=1\text{ for at most finitely many $n$}\right\}$ countable or uncountable?

Published on 24 Oct 2018 - 14:00

score 96 · Answer 12 · 2026-03-25 12:55:42

96

Views

Countability of a nonincreasing set

Published on 25 Mar 2026 - 12:55

score 117 · Answer 13 · 2026-03-26 06:29:46

117

Views

Can we have a cardinal exponent of any number?

Published on 26 Mar 2026 - 6:29

score 437 · Answer 14 · 2018-10-30 13:36:16

437

Views

Showing the set of 2$\times$2 matrices with integer entries are countable.

Published on 30 Oct 2018 - 13:36

score 92 · Answer 15 · 2026-03-25 09:48:50

92

Views

Dimension of vector space for irreducible representations

Published on 25 Mar 2026 - 9:48

List Question

Cardinality of $\{0,1\}^\mathbb{N}$

The set of sequences of $\Bbb N$ and $\mathcal{P} (\Bbb N)$ are equinumerous.

Let $X,Y,Z$ be nonempty sets. Then $|(X^Y)^Z|=|X^{Y\times Z}|$

Question about Hungerford's definition about cardinality

Suppose that $\aleph_0\le |A|<|B|$. Compare $|\mathcal {P}(A)|$ and $|\mathcal {P}(B)|$, $|A^B|$ and $|B^A|$, $|B^A|$ and $|B|$

Let $\mathfrak F$ be the set of injective mappings $f:\Bbb N\to\Bbb N$. Then $|\mathfrak F|=2^{\aleph_0}$

Injection from cardinal $\lambda$ to cardinal $\kappa$ implies $\lambda\leq\kappa$

Proving $A\subset B\implies |A|\leq |B|$

Examples of Commutative Semigroups Where the Cardinality of the Carrier Set is Greater Than $\mathfrak c$.

Question on injective-surjective functions, regarding cardinality of domain, codomain

Is $X=\left\{(x_n)_{n\in\mathbb{N}}\mid x_n\in\{0,1\},\forall n \wedge x_n=1\text{ for at most finitely many $n$}\right\}$ countable or uncountable?

Countability of a nonincreasing set

Can we have a cardinal exponent of any number?

Showing the set of 2$\times$2 matrices with integer entries are countable.

Dimension of vector space for irreducible representations

Trending Questions

Popular # Hahtags

Popular Questions