Suppose I am giving a math talk and I am going to write on the board Let A be a variable. What do I say while I write? Can I say Let's let A be a variable or should I write We let A be a variable and say the same thing?
I would say
Let x be variable and I would avoid using
A. The reason is that
a is already an overloaded letter in English and it's not immediately clear whether you are about to introduce a singular noun (e.g.,
Let a cat out of the house.) or the name of a variable.
Another useful phrase would be
Let lambda equal as it's likely you are about to introduce the definition of a variable. If you are talking about a variable that's in the middle of an equation, you could just use a declarative:
mu is variable or
c is constant.