3 ms·
> I'd call referring to these a serious misuse of terminology! Finite fields are altogether quite different. Sure, but also the important part of OP's argumen
by Hermitian909 5y ago
> I'd call referring to these a serious misuse of terminology! Finite fields are altogether quite different.
Sure, but also the important part of OP's argument seems to be that numbers be treated as members of the appropriate algebraic structure. Simply subbing in the correct terminology should fix the issue.
> I think the best short term for describing how machine integers work is to just say "modular arithmetic".
For addition this is correct, I don't believe it's correct for multiplication because of the negative integers. That is, the ring described by signed n-bit signed integers under multiplication and addition is not isomorphic to (Z_{2^n}, +, *).
- Sniffnoy 5y ago> For addition this is correct, I don't believe it's correct for multiplication because of the negative integers. That is, the ring described by signed n-bit signed integers under multiplication and addition is not isomorphic to (Z_{2^n}, +, *). No, it is. It is in fact just Z modulo 2^n, just with the choice of representatives being { -2^(n-1), ..., 2^(n-1)-1 } instead of { 0, ..., 2^n-1 }. This is pretty easy to check... do you have an example to the contrary?