List questions from cardinals | MathQA

Does cantor's diagonal argument to prove uncountability of a set and its powerset work with any arbitrary long column or row rather than the diagonal?

Published on 16 Apr 2026 - 11:31

Is $\aleph_{\alpha+1}^{\aleph_a} > \aleph_\alpha^{\aleph_a}$ true?

Published on 13 Apr 2026 - 16:58

Is the cardinality of an empty set comparable to some other sets by the definition?

Published on 11 Apr 2026 - 12:53

How many sub-sums of the harmonic series converge to a given $x$?

Published on 15 Apr 2026 - 7:09

Why is $\lim_{\eta \to \text{cf } \alpha} \omega_{\eta} = \omega_{\alpha}$?

Published on 15 Apr 2026 - 3:57

Proving $|\alpha^{<\omega}| < \kappa$ without Axiom of Choice

Published on 16 Apr 2026 - 11:10

How to linearly order the set of all subsets of real numbers?

Published on 09 Apr 2026 - 10:04

How can we prove that $\mathbb{N^2}$ has the same cardinality as $2\mathbb{N} + 1$

Published on 14 Apr 2026 - 16:36

Understanding limits with Cardinality

Published on 10 Apr 2026 - 10:30

Show that $\mathbb{R}$ and the open interval $(-1, 1)$ have the same cardinality.

Published on 16 Apr 2026 - 0:00

Disproving bijection between $\mathbb{N} $ and $[0,1) $

Published on 13 Apr 2026 - 6:06

On a property of gimel function $\gimel(\kappa)$ (Exercise 5.29 of Jech)

Published on 13 Apr 2026 - 16:34

Prove $[0,1)$ is of cardinality equal to $(0,1]$

Published on 09 Apr 2026 - 22:44

Does ZFC prove existence of proper class many $H_\kappa$ sets with $|H_\kappa|=\kappa$?

Published on 09 Apr 2026 - 2:08

Is it true that $\aleph(A_n)<c\implies \sum_{n\in\mathbb{N}}\aleph(A_n)<c$?

Published on 15 Apr 2026 - 10:16