Remark
143
[08X]Let \(A\) be a non-empty set, let \(f:A→\{ 0,1\} \) and \(g:A→\{ 1\} \) both given by \(f(x)=g(x)=1\) for each \(x∈ A\).
Let \(F,G\) respectively be the graphs: note that \(F=G\) (!) Will we say that \(f=g\) or not? We choose “not”, otherwise the concept of ”surjective” would not make sense.
For this reason in the definition we decided that the function is the triple ”domain”, ”codomain”, ”relation”.