On 24.10.2010 01:19, Daniel Peebles wrote:
Just out of curiosity, why do you (and many others I've seen with similar proposals) talk about additive monoids? are they somehow fundamentally different from multiplicative monoids? Or is it just a matter of notation? When I was playing with building an algebraic hierarchy, I picked a "neutral" operator for my monoids (I actually started at magma, but it's the same thing) and then introduced the addition and multiplication distinction at semirings, as it seemed pointless to distinguish them until you have a notion of a distributive law between the two.
I'm not sure that I understood your question completely. But I think it happens naturally. Authors of such proposals just don't think about monoids and abstract algebra. They think about R^n. It appears quite frequently (well it depends on domain) and Num&Co is useless. Proposals are born out of that frustration. Probably people who do care about distinction between additive and multiplicative monoids don't face that problem or it's