Every injection $f: A \to A$ for finite $A$ is surjective
45380
Surjectivity implies injectivity and conversely
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
105455
Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
74453
Injective and Surjective Functions
11202
If $g \circ f$ is injective, so is $g$
134104
Is there a Cantor-Schroder-Bernstein statement about surjective maps?
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
130363
Prove composition of two surjections is surjection
37308
Let $f:K\to K$ with $\|f(x)-f(y)\|\geq ||x-y||$ for all $x,y$. Show that equality holds and that $f$ is surjective.
124847
Is the set of surjective functions from $\mathbb{N}$ to $\mathbb{N}$ uncountable?
40566
Counting surjective functions
20303
A function $f\colon E\to F$ between finite sets is injective iff it is surjective iff it is bijective
28798
Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
64866
Proving a Composition of Functions is Bijective
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
145397
How to prove that for every $i$, $a_i = i$