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I think a shorter way to write that is to first note the downset representation of reals. Then your definition of min is just the set intersection and there's n
by arnarbi 7y ago
I think a shorter way to write that is to first note the downset representation of reals. Then your definition of min is just the set intersection and there's nothing more to show.
- Koshkin 7y agoTo be fair, reals have nothing to do with this - the 'min' makes sense - and is associative - in any ordered set (even partially ordered, if you accept that it may be undefined for some pairs).
- arnarbi 7y agoAbsolutely. Just going off the language used in the post which is maybe tailored to Brent's student audience.
- joppy 7y agoSo you define max([-∞, a]) =a, and define min(a, b) as max([-∞, a] ∩ [-∞, b])? Isn't this just shifting the problem elsewhere? For instance now you need to prove that the intersection of sets is of the form [-∞, a] or [-∞, b], which is fairly intuitive, but not more intuitive than the usual definition of min.