$A \setminus B$ is infinite, $B$ - finite. Proof that $(A \setminus B) \sim A$
42603
How can I prove that the cadinality of a set minus a finite number of elements of it is still the same as the original set?
55023
if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
66398
Union of a finite set and a countably infinite set is countably infinite
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
4912
Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$
20085
What's the cardinality of all sequences with coefficients in an infinite set?
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
41783
Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
66301
The cardinality of the set of countably infinite subsets of an infinite set
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
86926
Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
122947
What is the cardinality of the set of infinite cardinalities?