Construct disjoint sequence of infinite subsets of $\mathbb{N}$ whose union is not $\mathbb{N}$
50880
Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
59289
Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
153305
Adding subsets of regular cardinals (Jech p. 226)
133886
Existence of increasing sequence $\{x_n\}\subset S$ with $\lim_{n\to\infty}x_n=\sup S$
123357
Real Analysis - A sequence that has no convergent subsequence
69867
For each $\beta \in(0,1)$, give a sequence $\{a_j\}\subset(0,1)$ with $\prod (1-\alpha_j) = \beta $
156660
The set of all strictly increasing sequences of natural numbers
90074
Show that the sequence $1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,2,0,2,1,\cdots$ isn't periodic
120135
Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
67451
Building a bijection from a finite union of countable sets to $\mathbb{N}$
20085
What's the cardinality of all sequences with coefficients in an infinite set?
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
12404
Union of definable sets
89506
Union of disjoint sets : Equivalence relations
9651
Cardinality of cartesian product of an infinite set with N
66398
Union of a finite set and a countably infinite set is countably infinite