I am talking about a relation that is what Wikipedia describes as left-unique and right-unique. I never heard these terms before, but I have heard of the alternatives (injective and functional). The question is, *which terminology do you recommend*? Should I include short definitions? (The context is a text in the area of formal methods. I'm not sure if this helps.)

These are some trade-offs that I see:

- I think that
*left-unique*and*right-unique*are not widely known, but I'm not sure at all. *functional*is overloaded*injective*sounds too fancy (subjective, of course)*left-unique*and*right-unique*are symmetric (good, of course)

**Edit:** It seems the question is unclear. Here are more details. I describe sets *X* and *Y* and then say:

- now we must find an injective and functional relation between sets
*X*and*Y*such that... - now we must find a left-unique and right unique relation between sets
*X*and*Y*...

Which one do you recommend? What other information would you add? The relation does *not* have to be total. For example, various different ranges correspond to different 'feasible' relations. Technically I should not need to say that the relation does not have to be total, but will many people assume that it has to be total if I don't say it?

we must find an injective and functional relation between X and Y, and not define injective/functional. – rgrig Mar 11 '10 at 17:43