Comment by JohnHaugeland 3 months ago
The class is mathematics. In mathematics, numbers do not have types.
You also shouldn't try to mention INT_MAX, negative zero, rounding error, or other computer science topics which do not exist in mathematics.
Mathematicians generally work with sets, not types. The first thing you do after defining the reals is agree that the naturals, integers, and rationals are subsets. From a type theory perspective, they are all type ℝ, and, roughly, the naturals satisfy the proposition "n:ℝ is a natural number".
Mathematics has a lot of different theories and some small branches have different rules. I've done mod math for example (it was maybe one week of classes) where you don't get an infinite set of possible numbers. It isn't nearly as interesting as far as mathematicians are concerned (for good reason) so it isn't looked at much but those theories exist.
I am no Terry Tao, but I do have a degree in mathematics. Other than possibly in a class on numerical analysis, I don't remember anything resembling types.
We definitely spent more time discussing different kinds of infinity than we did discussing rounding error!
I can believe that the situation might be different in "applied mathematics" or definitely in "engineering mathematics" - but at least at Berkeley, the latter degree is in the College of Engineering, not under the Math Department at all.
Type theory comes from math. Numbers in math do in fact have types. Most of the time we ignore it but numbers in math have types. math also has the concept of max number rolling back to zero ogain something anyone who has studied types in math would know. Rounding error is studied in several different math fields.
negative zero isn't in any math I know of. It is only in obsolete computer science though.