There is given a countable set $A$. Prove that $(x+A)\cap A=\emptyset$ for some $x$
37398
Proof that$ (a+A)\cap A=\varnothing$ if $A$ is countable
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
43268
How to prove that the set of rational numbers are countable?
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
134770
For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
99656
Prove that the set of all algebraic numbers is countable
23442
Cardinality of the union of infinite and countable sets
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
66301
The cardinality of the set of countably infinite subsets of an infinite set
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
65768
What is the cardinality of the set of the empty set?
103314
Let $\{K_n \}_{n \in \mathbb{N}}$ be a collection of sets, where $K_n = [n, \infty)$. Why is $\bigcap_{n \in \mathbb{N}} K_{n}$ empty?
67066
Proof there is a 1-1 correspondence between an uncountable set and itself minus a countable part of it
138199
Proof explanation $A\setminus B = A \setminus B \cap A$
93771
Prove that for any set $A$ there is some $x \notin A$