Suppose $A$ and $B$ are two finite sets having same cardinality. Show that a function $ f:A \to B $ is one-one if it is onto
49592
Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto.
132868
Bijection between an infinite set and its union of a countably infinite set
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
65768
What is the cardinality of the set of the empty set?
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
96845
Question: Compare the cardinality between the sets $\Bbb R$ and $\Bbb N^{\Bbb N}$
158671
Cardinality of a set that consists of all existing cardinalities
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
101669
Cardinality of the Set of all finite subset of $\mathbb{R}$
125043
Show that F(A−B) is not necessarily a subset of F(A)−F(B).
85099
How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
149673
Cardinality of an infinite union of finite sets
88278
Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
93330
Cardinality of all cardinalities
2287
If a set is linearly independent, a finite subset of that set is also linearly independent
80421
Show that $a - b \mid f(a) - f(b)$