My view is quite unconventional, but I believe, computer science is a branch of mathematics that deals with large but finite structures (so they need an algorithmic description).
Compare with most of "legacy" mathematics, which studies countable structures (so the description can use arbitrary series).
Of course, there are larger sets, but they mostly serve as a theater (just like countable infinity is just a theater of computer science).
Finite sets in the rest of mathematics are sometimes considered uninteresting, but not so in computer science, where only very small sets (roughly of up to 32 elements, all subsets can be easily checked on a typical computer) are considered uninteresting.
Good example is number theory, which philosophically considers all natural numbers, regardless of size, to be equal type of objects. In computer science, the (although fuzzy) magnitude of numbers plays much bigger role.
Compare with most of "legacy" mathematics, which studies countable structures (so the description can use arbitrary series).
Of course, there are larger sets, but they mostly serve as a theater (just like countable infinity is just a theater of computer science).
Finite sets in the rest of mathematics are sometimes considered uninteresting, but not so in computer science, where only very small sets (roughly of up to 32 elements, all subsets can be easily checked on a typical computer) are considered uninteresting.
Good example is number theory, which philosophically considers all natural numbers, regardless of size, to be equal type of objects. In computer science, the (although fuzzy) magnitude of numbers plays much bigger role.