I agree completely. The only risk is that once you get to real analysis, your prof will yell at you for mixing notions of complexity and computability into your ideas of what a function is (happened to me).
A function is (at least formally) a relationship between two sets of things. It doesn’t matter whether there’s any sort of algorithm that lets you input an object from the domain and calculate the corresponding image under the function, or even an approximation. This came up when we were talking about Dedekind cuts or something like that so it’s very much not pedantry at all in that sort of context.
The main difference between pure math and computer science is that mathematicians assume uncountable sets exist and then use that to prove all sorts of nonsense that are not true in the physical or computable Universe.
Many CS papers, at least in machine learning, state an algorithm in terms of real numbers and use results from real analysis to prove properties of the algorithm.
Given that Cantor’s Diagonal Argument – which demonstrates the existence of uncountable sets – is the technique which underlies Turing’s solution to the Entscheidungsproblem, you might want to re-examine your assumptions.