| Thread Links | Date Links | ||||
|---|---|---|---|---|---|
| Thread Prev | Thread Next | Thread Index | Date Prev | Date Next | Date Index |
John Pryce wrote:
On 18 Sep 2010, at 23:15, Nate Hayes wrote:I speak against this. Ulrich's interior is better.Note that the topological interior, i.e., "proper subset," is already expressed efficiently in terms of Ulrich's relations for intervals A,B:( A \subset B ) and not ( A == B )Doesn't that make [2,3] interior to [1,3]?Well, it seems weird to me too, but there it is. You're an expert on quantified statements. Isn't it inescapable from the definition "B is a neighbourhood of each a in A" (eqn1)?I don't see Entire should be interior to Entire.
As you are so fond of quoting from George Corliss: if it even seems weird to you -- a seasoned mathemetician -- then "God help the casual user!"
The thing about definitions grounded in standard theory (and this theory has been around for roughly 100 years) is that, compared with ad-hoc definitions, you KNOW they can't lead to inconsistencies -- assuming math itself is consistent.
This is a reason I think P1788 might want to investigate sticking to compact intervals, instead.... which if you remember was one of my first choices.
Nate