Comment by Chinjut

The fixed-size signed types of C etc are no more the actual integers, and no less modular arithmetic, than the fixed-size unsigned types. They both implement the exact same modular arithmetic for +, -, and *. It's only for other operations (ordering comparisons, or / and % which in turn are defined in C in terms of ordering structure, as in rounding towards zero) where they differ. And in either case, that ordering structure is not one commonly encountered anywhere outside of the context of fixed size computer arithmetic.

Ask an ordinary person what 3 * (1/3) or 3 * (-1/3) should come to, and they aren't going to say any of the results that you get in C for either signed or unsigned int types.