Prove that a function $f:\Bbb{N}\rightarrow \Bbb{Q}$ is injective.
133083
Injectivity and surjectivity of a recursive function
141166
How to show that when the linear transformation $\Phi =\psi \circ \phi : E \rightarrow G$ is injective, then $\phi$ is also injective?
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
121886
Proving image of $f:D^n\rightarrow \mathbb{R}^n \;$ contains $\;D^n$
6023
Surjectivity of Composition of Surjective Functions
78698
Prove if $f$ has a right inverse function: $f\circ g=id_x$ $\iff$ $f$ is onto $Y$
52565
Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
133699
Proving that there is a bijection between $A$ and $B$.
148500
Understanding this theorem and how to go about proving it surjectivity?
109498
Linear maps $f: M_n \longrightarrow \mathbb{R}$ such that $f(AB) = f(BA)$
71156
$f(x) = \frac {ax+b}{cx+d}$ , bijection $f: \Bbb R \to\Bbb R$?
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
28111
Let $f:[1,10]\to \Bbb{Q}$ be a continuous function and $f(1)=10,$then $f(10)=?$
10307
Show the inverse of a bijective function is bijective
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
28798
Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$