How do I say to express giving a definite value/choice to a variable/possibilities in math or physics?

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 y."?

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)."?

• Not a direct answer to your question, but see: ell.stackexchange.com/questions/81833/… – Adam Mar 21 '16 at 19:46
• I'd personally use choose (e.g., We choose a certain value of x to satisfy a certain condition; We choose x to be 2 so/such that y = 5 (because y = x+3). I refrain from posting an answer because I'm not sure about your Lorentz frame example. – Damkerng T. Mar 21 '16 at 20:52
• I originally wanted to and have used "choose" in this kind of contexts naturally for long without doubt. But yesterday I posted a question in StackExchange to ask the usage of "choose", then someone replied me using "choose" in that way is incorrect. The correct way according to her response should be "choose 2 to be x". But I prefer to find a verb which can let the variable/possibilities prior to the value/choice. – Captain Bohemian Mar 21 '16 at 21:10
• "Choose x to be 2" is better than "choose 2 to be x." I've edited below and posted an answer there. – WBT Mar 22 '16 at 4:00

The shortest answer is let as in:
Let x=2.
Because y=x+3,
y=5.

This is also called variable assignment and you can talk about assigning a value to a variable, especially in the context of implementing your math/physics with some computer programming. This particular verb doesn't work as well for your nonvariable examples like gauge condition, unless you're discussing storage of that value in a variable in computer code.

The terms you ask about, fix and set, could also be used, and imply that you can control the value you are putting in. For example, if we fix/set the weight of this container to 10 kg, it will take 30 N of force to move it across this surface. The two terms are basically interchangeable in this context, but fix has a slightly greater implication that you're putting in some value that's somehow better than some existing value.

Choose is OK too, and per comments (as well as this question) it's apparently what you prefer. When you use "choose" (in whatever conjugated form is appropriate) you should specify who is doing the choosing.

Compared to fix, set, or choose, take (the companion verb of also-acceptable-but-more-passive given) has more of a connotation that you are reading some value, e.g. from a real-world measurement or other exogenous source. For an example, if you're explaining the ideal gas law you can say "if we take the temperature to be 25 degrees Celsius, we can see from this equation that..."

• What do you mean by "in whatever conjugated form is appropriate"? Do you mean both "choose x to be 2" and "choose 2 to be x." are appropriate? – Captain Bohemian Mar 22 '16 at 19:01
• No, I mean "we choose x to be 2" (present tense) is appropriate if you're doing a live demonstration at the board, "we chose x to be 2" (past tense) is appropriate if you're writing in a paper about how you set up the first parts of an experiment, "you will choose the Ace of Spades" if you're a future-predicting magician, "he would have chosen the passcode to be 1234" if you're considering possibilities from the past, etc. Reversing the order of x and 2 is not related to conjugating the verb "choose." – WBT Mar 22 '16 at 19:27
• Thank you. It turns out "conjugate" in Grammar refers to the tenses of a verb. – Captain Bohemian Mar 22 '16 at 21:55
• So is "choose" also the best word choice for my latter two examples? That is to say, saying "I choose the gauge condition to be the Lorentz gauge." is better than "I fix/take/set the gauge condition to be the Lorentz gauge." and saying "I choose the coordinate system to be the Lorentz frame." is better than "I fix/take/set the coordinate system to be the Lorentz frame."? – Captain Bohemian Mar 22 '16 at 22:01