Prove that the map $f:A\rightarrow B$ is injective if and only if $f$ has a left inverse.
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse
42941
Pair of adjoint functors and showing that two certain maps are inverses
16610
Surjectivity of a map from a space to itself
133699
Proving that there is a bijection between $A$ and $B$.
49882
Proving $f(x,y,z)=\big(\frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \big)$ is injective
152438
Is the composition of two injective functions injective?
80421
Show that $a - b \mid f(a) - f(b)$
64866
Proving a Composition of Functions is Bijective
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
14277
Proving $f(x)=x\cdot |x|$ is a bijection
10307
Show the inverse of a bijective function is bijective
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
76674
Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?
93964
Proving that $f$ is a bijection from $N$x$N$ to $N$.
25997
Conditions Equivalent to Injectivity
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement