In math or physics, there are some variables or possibiliies to be specified. I wonder how to express giving a definite value/choice for a variable/ possibilities. In the following I just give a few examples to clarify what I intend to ask.
The simplest example is a function, say,
y=f(x)=x+3, which is a variable
(y) varying with another variable
(x). When I want to say "I give
x a certain value to get a value for
y", how can I say in a concise way? Can I say, for instance, "I fix/take/set
x to be 2 to get 5 for
Another example is the gauge condition, which is a condition which can be adjusted without affecting physics. Can I say "I fix/take/set the gauge condition to be the Lorentz gauge (a gauge choice in electromagnetics)."?
Still another example is coordinate systems, which are the reference frames one takes to describe what (s)he observes. Can I say "I fix/take/set the coordinate system to be the Lorentz frame (a reference frame in relativity)."?