If $A$ is infinite, $B$ is finite and $B \subset A$ and $C=A\setminus B$. Is there bijection between A and C?
49709
Suppose $X$ is infinite and $A$ is a finite subset of $X$. Then $X$ and $X \setminus A$ are equinumerous
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
88201
Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective.
139078
Infinite partition of $\mathbb N$ by infinite subsets
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
119084
How many ordered pairs $(A,B)$ they are if $A$ and $B$ are subsets of $\{ 1,2,3,4,5 \}$ such that $A \cap B = \{1\}$?
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
27188
Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
32340
Continuous bijections and their inverses
145428
Set $A$ is countably infinite if and only if there exists a bijection $f: \mathbb{N} \rightarrow A$
151928
How to prove that $N\setminus A$ is finite?
85099
How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
107207
$A\subseteq B\subseteq C$ ring extensions, $A\subseteq C$ finite/finitely-generated $\Rightarrow$ $A\subseteq B$ finite/finitely-generated?
24372
Infinite Set is Disjoint Union of Two Infinite Sets