Who first defined functions as binary relations?

Question

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.

Ah. yes, I see, in 1921! Thank you, Don! https://en.wikipedia.org/wiki/Ordered_pair#Kuratowski's_definition — Sergei Akbarov, Oct 17 '19 at 01:00
@DonThousand , is it possible that Cantor used another trick for showing that functions are sets, before Kuratowski? — Sergei Akbarov, Oct 17 '19 at 01:04
Not sure. I would read through Cantor's paper on the devil's staircase to see how he defines it. — Rushabh Mehta, Oct 17 '19 at 01:09
Relevant : Bertannd Russell. See Principles (1903) , §254 : "In its most general form, functionality does not differ from relation. […] But this most general idea of a function is of little use in mathematics. There are two principal ways of particularizing the function: first, we may confine the relations to be considered to such as are one-one or many-one, i.e. such as give to every referent a unique relatum." — Mauro ALLEGRANZA, Oct 18 '19 at 13:47
Into Principia (1910-13), Russell & Whitehead developed a mathematical theory of relations, where relations are collections of ordered pairs: it was independent of the theory of classes, because the book is "pre-Kuratowski" and thus there is no formal reduction of the concept of pair to that of sets. — Mauro ALLEGRANZA, Oct 18 '19 at 13:49
Norbert Wiener "in his Harvard Ph.D. dissertation (June 1913, when he was 18 years: comparison of the work of Ernst Schröder with that of Alfred North Whitehead and Bertrand Russell), [discovered] the essential results of which were published as Wiener (1914). […] he was the first to state publicly that ordered pairs can be defined in terms of elementary set theory. Hence relations can be defined by set theory, thus the theory of relations does not require any axioms or primitive notions distinct from those of set theory." — Mauro ALLEGRANZA, Oct 18 '19 at 13:52
@MauroALLEGRANZA , thank you! So the impression is that Wiener was the first one who stated that functions are sets. — Sergei Akbarov, Oct 18 '19 at 15:24
The first one that discovered/developed the way to represent function as sets. — Mauro ALLEGRANZA, Oct 18 '19 at 15:27
We have also to take into account Frege's concept of Course-of-Values (Werteverlauf), more or less the modern concept of graph of a function. — Mauro ALLEGRANZA, Oct 18 '19 at 15:29

Who first defined functions as binary relations?

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