Question

Is the proper segment of a TOSET is initial segment?

score 45 · Answer 1 · 2026-04-12 17:53:49

45

Views

Is the proper segment of a TOSET is initial segment?

Published on 12 Apr 2026 - 17:53

score 153 · Answer 2 · 2021-04-11 03:41:38

153

Views

Why $\epsilon \aleph_0 =\epsilon$?

Published on 11 Apr 2021 - 3:41

score 127 · Answer 3 · 2021-04-11 09:16:40

127

Views

Bijection between the power set of $\mathbb R$ and $\mathbb R^{\mathbb R}$

Published on 11 Apr 2021 - 9:16

score 328 · Answer 4 · 2026-04-06 11:57:45

328

Views

Are all cardinals of the form $\aleph_0$ or $2^\alpha$?

Published on 06 Apr 2026 - 11:57

score 288 · Answer 5 · 2021-04-16 21:23:02

288

Views

Let $S \subseteq \mathbb{R}^2$ and the distance of any two points in $S$ is rational. Prove $S$ is a countable set.

Published on 16 Apr 2021 - 21:23

score 97 · Answer 6 · 2021-04-16 22:54:30

97

Views

Find the cardinality of the set $\{ m + \sqrt 5 n + \sqrt3 p : m, n, p \in\mathbb Q\}.$

Published on 16 Apr 2021 - 22:54

score 129 · Answer 7 · 2026-04-12 23:30:18

129

Views

if $f(x)$ is a polynomial with complex coefficients, prove that if $|f(x)|\leq 1$ for all $x\in \mathbb{C}$, then $f$ is a constant polynomial.

Published on 12 Apr 2026 - 23:30

score 51 · Answer 8 · 2026-04-13 10:58:27

51

Views

Map from set to its subset

Published on 13 Apr 2026 - 10:58

score 95 · Answer 9 · 2021-04-18 21:16:56

95

Views

If $w$, $x$, $y$, and $z$ are real numbers with $w < x$ and $y < z$, is the cardinality of the closed interval $[w,x]$ the same as that of $[y,z]$?

Published on 18 Apr 2021 - 21:16

score 231 · Answer 10 · 2026-04-12 13:10:42

231

Views

Does this set have cardinality $\beth_\omega$? And if so, how does it require the Axiom of Replacement to construct?

Published on 12 Apr 2026 - 13:10

score 1k · Answer 11 · 2021-04-19 02:46:40

1k

Views

Sets having the same cardinality

Published on 19 Apr 2021 - 2:46

score 84 · Answer 12 · 2021-04-19 20:15:42

Prove that the set, upper half unit circle, $S=\{(x,y) \in \mathbb{R}\times \mathbb{R} : y=\sqrt{1-x^2}, y>0\}$ has cardinality $\mathfrak{c}$.

score 105 · Answer 13 · 2021-04-25 18:17:52

105

Views

Show that $X\times Y$ has cardinality $c$

Published on 25 Apr 2021 - 18:17

score 54 · Answer 14 · 2026-03-26 22:58:20

54

Views

What is the cardinality of the set of possible wavefunctions $\Psi: (\mathbb{R}^3 \to \mathbb{R}) \to \mathbb{C}$?

Published on 26 Mar 2026 - 22:58

score 214 · Answer 15 · 2026-04-12 02:56:59

214

Views

Why does $|A|\le|B|$ imply $|\mathcal{P}(A)|\le|\mathcal{P}(B)|$? (Use elementary notations; for beginners to advanced math)

Published on 12 Apr 2026 - 2:56

List Question

Is the proper segment of a TOSET is initial segment?

Why $\epsilon \aleph_0 =\epsilon$?

Bijection between the power set of $\mathbb R$ and $\mathbb R^{\mathbb R}$

Are all cardinals of the form $\aleph_0$ or $2^\alpha$?

Let $S \subseteq \mathbb{R}^2$ and the distance of any two points in $S$ is rational. Prove $S$ is a countable set.

Find the cardinality of the set $\{ m + \sqrt 5 n + \sqrt3 p : m, n, p \in\mathbb Q\}.$

if $f(x)$ is a polynomial with complex coefficients, prove that if $|f(x)|\leq 1$ for all $x\in \mathbb{C}$, then $f$ is a constant polynomial.

Map from set to its subset

If $w$, $x$, $y$, and $z$ are real numbers with $w < x$ and $y < z$, is the cardinality of the closed interval $[w,x]$ the same as that of $[y,z]$?

Does this set have cardinality $\beth_\omega$? And if so, how does it require the Axiom of Replacement to construct?

Sets having the same cardinality

Prove that the set, upper half unit circle, $S=\{(x,y) \in \mathbb{R}\times \mathbb{R} : y=\sqrt{1-x^2}, y>0\}$ has cardinality $\mathfrak{c}$.

Show that $X\times Y$ has cardinality $c$

What is the cardinality of the set of possible wavefunctions $\Psi: (\mathbb{R}^3 \to \mathbb{R}) \to \mathbb{C}$?

Why does $|A|\le|B|$ imply $|\mathcal{P}(A)|\le|\mathcal{P}(B)|$? (Use elementary notations; for beginners to advanced math)

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