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