/sci/ - Science & Math

I still don't really get what a semiring is. All I really understand is that rings, semirings, fields, and their sigma versions are just sets with defined properties that have useful applications. Most of these classes have logical enough properties (being closed under X operation) but how in the hell does anyone just decide that they'll make a class called a semiring and say "alright this one will be closed under intersection and also let's have the proper difference of any two subsets be able to equal the countable union of a sequence of disjoint subsets."

And then sigma ring generated from the set of all intervals, which is "clearly" a semiring, is somehow the Borel Algebra. I'm tired of being a brainlet, anons.