Mathematicians often use the phrase "Denote the object X by the symbol Y". For example, I usually denote the set of numbers 1,2,3,4... by the boldface letter N. However a friend of mine uses a different phrase I have never seen before: "Let us write N for the set of numbers 1,2,3,4...". Is this a correct usage of the verb "write"?
NOTE: The "let us" is also awkward, but it is standard mathspeak and hence I consider it allowed on the basis of common usage. This is not the case for "write X for Y", which I have never read elsewhere.