$X$ and $Y$ have the same cardinality if and only if there exist a bijection from $X$ to $Y$?
7871
Are "if" and "iff" interchangeable in definitions?
120562
If A is an infinite set and B is at most countable set, prove that A and $A \cup B$ have the same cardinality
157920
Can I define $y=y(x)$?
82947
Undecidable cardinality
45216
Cardinality of $[0,1]$
3636
Are any two uncountable sets similar to each other?
85099
How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
40586
There exists an injection from $X$ to $Y$ if and only if there exists a surjection from $Y$ to $X$.
138283
$|(a,b)| = |\Bbb R|$ ? Cardinality of any open interval
97697
Countable union of sets of cardinality $c$ has cardinality $c$
13398
Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
158671
Cardinality of a set that consists of all existing cardinalities
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
32081
The dual version of trichotomy of cardinality without AC
79568
Cardinality of the set $D$
156783
$\mathbb R$ has the same cardinality of any interval