An endomorphism is one where the domain and codomain are the same.
The following are endomorphisms:
\(f(x)=0\)
\(f(x)=x\)
\(f(x)=cx\)
The following are not endomorphisms
Converting natural numbers to integers
\(f(x)=x+1\)
An endomorphism which is also an isomorphism
The following are automorphisms:
\(f(x)=x\)
\(f(x)=cx\)
The following are not automorphisms
\(f(x)=0\)
\(f(x)=x+1\)
Converting natural numbers to integers