This view of CS seems to exclude two of the most important topics - undecidability and NP hardness.
the main techniques in both of these areas require infinite sets. For undecidability, it’s the infinite set of proposed halting problem TMs, and for NP hardness, it’s the infinite set of solutions to a given problem.
Runtime analysis also requires numbers larger than 2^64 — any algorithm which is not O(n) is practically faced with these numbers. Sorting, matrix multiplication, etc.
Yes you can have mathematical techniques in CS, I am talking about focus or emphasis of the discipline. Obviously, there are gonna be subjects on the fringes (set theory is another example).
Similar to what you say, mathematical analysis uses uncountable sets (especially the ones above reals). But they're just a theater, not the actors. The actors are the countable sets - sequences, continuous functions..
And I think similar situation is in CS, where infinity, while useful, is just a theater to uncover properties of medium-sized finite objects.
For many people, philosophy is kind of "obvious babbling". But as you can see, that's what we engage here. It's interesting to think about this in the context of Skolem's paradox - I think the two views (the mathematical and the CS emphasis on nature of numbers) are actually equally valid.
I disagree my friend. CS is math; they aren’t separate. The topics are at the core, not on the fringe. And if we need infinity to understand the small objects, then infinity is more important than the small objects themselves.
the main techniques in both of these areas require infinite sets. For undecidability, it’s the infinite set of proposed halting problem TMs, and for NP hardness, it’s the infinite set of solutions to a given problem.
Runtime analysis also requires numbers larger than 2^64 — any algorithm which is not O(n) is practically faced with these numbers. Sorting, matrix multiplication, etc.