terminology - Do you need to say what left-unique and right-unique means?

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:

1. now we must find an injective and functional relation between sets X and Y such that...


2. 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?