::I just looked up Bourbaki's "Theory of sets" in Google books (in English translation). The definition of an injective mapping is on page 84. The definition gives both "injective" and "injection" but not "injectivity", and only gives the definition for mappings, not relations. So I do not see evidence there that "injection" is derived from "injectivity", nor that the definition was given simultaneously for functions and relations. As always, I would be glad to be proved wrong about this via references to prior usage of the terminology. — Carl ( ·