$f,g: \mathbb{N} \rightarrow \mathbb{N} $, where $f(n)=g(2n)$. Prove that if $f$ is surjective, $g$ is not injective.
35953
Prove that a function is not injective
157756
Examine if function $f:\mathbb{R^2}\rightarrow \mathbb{R^2}$ which is defined as $f(x,y)=(2x-y,x-4y)$ is bijective. If bijective, find $f^{-1}$.
130363
Prove composition of two surjections is surjection
31391
bijection between $\mathbb{N}$ and $\mathbb{N}\times\mathbb{N}$
40993
Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
63146
Proof of properties of injective and surjective functions.
85612
Let functions $ f: A \to B$ and $g: B \to A$, suppose that $ g \circ f = i_A$. Prove that if $f$ is onto, then $g$ is one-to-one
16413
Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.
120877
$A$ abelian variety. Is the multiplication by $n_A$ surjective?
46971
Number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$
53168
Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
152057
Let $(X,d)$ be a compact metric space. Let $f: X \to X$ be such that $d(f(x),f(y)) = d(x,y)$ for all $x,y \in X$. Show that $f $ is onto (surjective).
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
74453
Injective and Surjective Functions
47709
If $n\mid m$ prove that the canonical surjection $\pi: \mathbb Z_m \rightarrow \mathbb Z_n$ is also surjective on units
45991
Why $f\colon \mathbb{Z}_n^\times \to \mathbb{Z}_m^\times$ is surjective?
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.