Q:

Mathematical Jargon when choosing for determinacy

What is the usual expression a mathematician uses when he has to make a choice in order limit an over-determined structure, in order to continue his argument?
For instance, when a structure is over-determined, a law may be true up to a sign. Deriving the law may require the mathematician/physicist to choose either sign and follow the formalism. This choice may become convention, eg. Hook's law for linear elasticity.
This is trivial and embarrassing, but I cannot remember nor can I find the answer on google. It has to be something along the lines of, "For the sake of determinacy, choose x from" or "For the sake of certainty, let x be." None of these sound quite natural though. Please help.

A:

"For the sake of argument, and without loss of generality" is quite good.
Thanks for all the comments and to Edwin Ashworth in particular.
EDIT Thanks, Andreas, it is "definiteness."

