'non-injective' originates from the English prefix 'non-' (from Latin 'non') meaning 'not', combined with the adjective 'injective', which itself is formed from the verb 'inject' + adjectival suffix '-ive'. 'Inject' ultimately goes back to Latin 'injicere' (in- 'into' + jacere 'to throw').

'injective' developed in English from Latin 'injicere' → Old/French forms (e.g. French 'injecter') → English 'inject' (to put or throw in) and later the adjectival form 'injective' was coined; 'non-injective' is the productive negation using the prefix 'non-' added to that adjective, used in mathematics to mean 'not injective'.

Originally 'inject' meant 'to throw or put into'; from this the adjective 'injective' was coined (and later specialized in mathematics to describe one-to-one mappings). 'Non-injective' now specifically means 'not one-to-one' in the mathematical sense.