3 msΒ·
> I believe you can do bold in Unicode. (see: ππ¨π₯π) As far as I know HN has never supported bold as a markup style. Oh, I think you're right, I'd forgotten
by Sniffnoy 3y ago
> I believe you can do bold in Unicode. (see: ππ¨π₯π) As far as I know HN has never supported bold as a markup style.
Oh, I think you're right, I'd forgotten. Grr, HN's limited subset of Markdown is quite annoying sometimes. Well, I'm going to be lazy and just write "R".
> I'd like to know more about the sets you refer to, β[Ξ΅] and β(Ξ΅), but I don't recognize them. Do they have names I can search for?
No, they don't, that's part of my point -- that you don't need to use recognized systems with names, you can use the usual constructions (or unusual constructions...) to make your own in the way that mathematicians always do. I mean I guess they sort of have names in that the notation would be pretty understandable to most everyone, although pronouncing it is annoying in that they'd both most typically just be pronounced "R adjoin epsilon", although I guess you could say "ring-adjoin" or "field-adjoin" to disambiguate. But note that there's plenty of other variants one could make as well, not just these.
Basically go learn some abstract algebra, is what I would say. Or go read about ring adjunction (and polynomials) or field adjunction (and rational functions).
Btw, I wouldn't describe these as "sets", that's not really the appropriate word to use here. When we talk about systems of numbers, we are, well, talking about systems, or algebraic structures -- rings, fields, ordered rings or fields, topological rings or fields, etc. To say "set" implies that what is important is the elements of these things, the contents; but these elements have no meaning on their own, they're given meaning by the structure -- the permitted operations, relations, etc. (Addition, multiplication, negation, less than or equal to...) Formally, an algebraic structure is a tuple, with the base set being just the first element of that tuple, even if we typically abuse notation and use the same symbol to refer to the set and the structure on that set.
Um, hope that's helpful?