The words "surjective" and "bijective" have transparent etymologies: "sur" is French for "on" (as in, "onto"), and "bi" hints at the two-way nature of bijective functions.

"Injective" is more of a mystery. All functions "inject" every element of their domain into the target space, and there is nothing about the word "inject" (in English) that suggests two things can't be injected into one thing. (E.g., you can be given two different injections at the same point on your arm.) Is there a sensible etymology or reason that this word came to mean "one-to-one"?

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    $\begingroup$ hsm.stackexchange.com/questions/4929/… $\endgroup$ Oct 8 '19 at 5:24
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    $\begingroup$ How is "surjective" any more transparent than "injective"? There's nothing about "sur" or English "onto" to suggest that every element of the codomain is the image of some element of the domain. If I say "the people got omto the bus" does that imply that there are now no empty seats? $\endgroup$
    – bof
    Oct 8 '19 at 7:23

Injection is from late latin iniectio, -onis, derived from inicio, -is, -ieci, -iectum, -ĕre: "to throw in", "to put in", "to let in".

There kind of is the idea of just displacing objects somewhere else, thus preserving their identities. Though I doubt common latin used to have a ready made term for this kind of subtlety.


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