[l33t2328]

I’d argue math is actually (a proper subset of) CS.

[ravi-delia]

Math is at it's broadest the study of formal systems. Computer science is the study of a particular formal system. While it is a powerful enough system to contain all of math within it, there are many such systems nested within each other. Is the Turing machine formalism more powerful? No. Is it more efficient or intuitive? Also no. It requires axiomatic reasoning to construct, and then reproduces it internally. Math and CS are set equal, but one predefines an entry point and the other does not. From the human perspective math gives rise to CS, which is just one of math's many children.

[l33t2328]

I’d argue that logic is a subfield of computability theory, and so by extension we (in CS) absorb math.

[ravi-delia]

Like I said, you can indeed construct logic through CS! But you can also obviously construct CS from logic. You can also construct logic through the natural numbers, so number theory absorbs math and by extension CS? Fact is anything reasonably complex can replicate everything else. Exactly one of these fields, however, is specifically carved out as the study of any formal system, and it isn't CS.

[l33t2328]

I’m arguing that logic is a subfield of CS, so “constructing” CS “from” logic isn’t a contradiction.

[qiskit]

CS only involves computable numbers ( Turing ) which are a subset of real numbers. By definition CS is a subset of math, not vice versa.

[Koshkin]

But the real numbers cannot be faithfully represented in a computer!

[l33t2328]

So? Neither can the list of possible computer programs, yet CS studies them

[Koshkin]

It does not look like CS studies the real numbers.

[l33t2328]

Each real number can be represented as a subset of the natural numbers. CS surely studies these.

[Koshkin]

But not the representations themselves (which is what's important in this case).