Prove that if $|X|=\aleph _0$ then there exist a family of sets, $\mathcal{F}$, of subsets of $X$, s.t $|\mathcal{F}|=\aleph$
2403
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
123613
Double Complement of a set proof
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
57868
Prove $\tau$ is cofinite on $X$ iff $(X,\tau)$ is $T_1$-space and any infinite subset of $X$ is dense in $(X, \tau)$
156006
Cardinality of set containing all infinite subsets of $\mathbb{Q}$
41477
Prove $f(S \cap T) \subseteq f(S) \cap f(T)$
117561
A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
75614
Proving that $n|m\implies f_n|f_m$
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
129813
Is there an easy proof for ${\aleph_\omega} ^ {\aleph_1} = {2}^{\aleph_1}\cdot{\aleph_\omega}^{\aleph_0}$?
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
66301
The cardinality of the set of countably infinite subsets of an infinite set
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
109070
Question about the proof of the distributive property for sets