Proof that an injection between sets in one direction implies existence of a surjection in the opposite direction - cardinality
40586
There exists an injection from $X$ to $Y$ if and only if there exists a surjection from $Y$ to $X$.
82003
Bijection between sets of ideals
77791
Proving an inclusion related to algebraic sets and interpreting it
154230
In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists
109070
Question about the proof of the distributive property for sets
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
122271
A subset of a transitive set is transitive
111032
Proof of Sets involving the Cartesian Product
93771
Prove that for any set $A$ there is some $x \notin A$
118595
Proving that a set is countable by finding a bijection
37951
proof detail concerning bijection between a set and its power set
37331
Prove that every set with more than one element has a permutation without fixed points
60359
Proving that these two sets are denumerable.
97878
Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
46698
Showing a set is closed under inverses
2396
Order-preserving injections of ordinals into $[0,1]$