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
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