Admitedly, I don't know what "university notation" is. This site University Maths Notes - Set Theory - Notation for Set Theory

has examples of interval notation...

For the first example, the range of y = x^(-1) = 1/x is all real numbers except zero. So you could write

D = ℝ \ {0}, or

D = {y : y ∈ ℝ and y =/= 0}, or

D = (-∞, 0) U (0, ∞),

depending on the prof.