Question

Proof that $\mathbb{R}$ is not countable

score 181 · Answer 1 · 2026-04-11 18:51:20

181

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Proof that $\mathbb{R}$ is not countable

Published on 11 Apr 2026 - 18:51

score 87 · Answer 2 · 2021-01-10 17:34:54

87

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How can we show that the set of all polynomials with integer coefficients denumerable?

Published on 10 Jan 2021 - 17:34

score 34 · Answer 3 · 2021-01-10 21:54:09

34

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Let $f : N → Y$ be a map having right inverse $g$. Prove that $Y$ is at most countable?

Published on 10 Jan 2021 - 21:54

score 173 · Answer 4 · 2026-04-12 04:13:06

173

Views

Stuck with a proof regarding cardinality

Published on 12 Apr 2026 - 4:13

score 41 · Answer 5 · 2021-01-11 19:11:15

41

Views

Prove that for $S$ a maximal mean less subset, $|S|=\aleph$.

Published on 11 Jan 2021 - 19:11

score 71 · Answer 6 · 2026-04-12 08:53:04

71

Views

Is there a one-to-one corrospondence between integer functions and the reals?

Published on 12 Apr 2026 - 8:53

score 57 · Answer 7 · 2026-04-12 03:24:16

57

Views

Is the cardinality of the topology of a separable infinite metric space uncountable

Published on 12 Apr 2026 - 3:24

score 71 · Answer 8 · 2026-04-10 23:27:39

71

Views

Cardinals proof |A| ≤ |B| iff |B| ≥ |A|

Published on 10 Apr 2026 - 23:27

score 58 · Answer 9 · 2021-01-15 18:18:32

58

Views

Proof that vector spaces $k^M$ and $k^{(M)}$ are not isomorphic

Published on 15 Jan 2021 - 18:18

score 36 · Answer 10 · 2021-01-16 07:17:12

36

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If $B \subseteq A$ and $f:A \xrightarrow{1-1} B$, prove that $\bigcap_{n \lt \omega}f^n[A]=\bigcap_{n\lt \omega}f^n[B]$

Published on 16 Jan 2021 - 7:17

score 44 · Answer 11 · 2021-01-17 08:52:08

44

Views

Direct Proof: $A\subseteq\bigcap_{n\lt\omega}f^n[A]\cup\bigcup_{n\lt\omega}f^n[A]\setminus f^n[B]\cup \bigcup_{n\lt\omega} f^n[B]\setminus f^{n+1}[A]$

Published on 17 Jan 2021 - 8:52

score 148 · Answer 12 · 2026-04-12 23:47:59

148

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Cardinality of Set and its Power Set Singleton

Published on 12 Apr 2026 - 23:47

score 102 · Answer 13 · 2021-01-18 00:21:03

102

Views

Prove that $ | \mathcal {P} (\mathbb N) | \le | \mathbb R | $.

Published on 18 Jan 2021 - 0:21

score 47 · Answer 14 · 2026-04-11 19:51:09

47

Views

Could we define cardinal number on well-founded equality?

Published on 11 Apr 2026 - 19:51

score 45 · Answer 15 · 2021-01-18 12:30:40

45

Views

Lebesgue measure of sets with cardinality greater than $ℵ_1$

Published on 18 Jan 2021 - 12:30

List Question

Proof that $\mathbb{R}$ is not countable

How can we show that the set of all polynomials with integer coefficients denumerable?

Let $f : N → Y$ be a map having right inverse $g$. Prove that $Y$ is at most countable?

Stuck with a proof regarding cardinality

Prove that for $S$ a maximal mean less subset, $|S|=\aleph$.

Is there a one-to-one corrospondence between integer functions and the reals?

Is the cardinality of the topology of a separable infinite metric space uncountable

Cardinals proof |A| ≤ |B| iff |B| ≥ |A|

Proof that vector spaces $k^M$ and $k^{(M)}$ are not isomorphic

If $B \subseteq A$ and $f:A \xrightarrow{1-1} B$, prove that $\bigcap_{n \lt \omega}f^n[A]=\bigcap_{n\lt \omega}f^n[B]$

Direct Proof: $A\subseteq\bigcap_{n\lt\omega}f^n[A]\cup\bigcup_{n\lt\omega}f^n[A]\setminus f^n[B]\cup \bigcup_{n\lt\omega} f^n[B]\setminus f^{n+1}[A]$

Cardinality of Set and its Power Set Singleton

Prove that $ | \mathcal {P} (\mathbb N) | \le | \mathbb R | $.

Could we define cardinal number on well-founded equality?

Lebesgue measure of sets with cardinality greater than $ℵ_1$

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