I am talking about a relation that is what Wikipedia describes as [left-unique and right-unique][1]. 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?

  [1]: http://en.wikipedia.org/wiki/Relation_(mathematics)#Special_types_of_binary_relations