In modern textbooks on set theory, for example in Thomas Jech's Set theory, p.11, functions are defined as "graphs", i.e. binary relations with the property $$ (x,y)\in f\ \&\ (x,z)\in f\quad\Rightarrow\quad y=z, $$ while the definition of binary relation is based on the construction of orded pair as the set $$ (a,b)=\{\{a\},\{a,b\}\}. $$ (So this is the standard trick that shows that functions are special cases of sets.)
Can anybody enlighten me who was the author of this idea?
Was that Cantor?
Edit: I am not asking why this (Kuratowski's) construction gives a proper definition of ordered pair. My question is who (and when) first defined functions as binary relations (and showed that functions are sets).
Edit 2: Ladies and gentlemen, I suppose, before closing this question it would be good to propose an answer.