Claudio and JB. You both raised similar arguments about why the empty 
interval is basically the same whether it is [9:00, 9:00) or [10:00, 
10:00), i.e. the important factor is that it's empty, not what it's 
end-point is.

if you look at the interval [9:00, 9:00) as the limit of [9:00, 9:00 + 
epsilon) as epsilon goes to zero, you have a situation where each of the 
intervals on the way to the limit (i.e. epsilon > 0) overlaps [9:00, 
10:00) and is _not_ contained in [10:00, 11:00). i'm arguing that the 
limit [9, 9) should be interpreted in a way that is consistent with the 
behavior of the sequence that defines it [9, 9 + e). this is what i mean 
by _intuitive_ behavior. i.e. [9:00, 9:00) overlaps [9:00, 10:00) and is 
not contained in [10:00, 11:00).

in any case, my proposed solution involves allowing both open and closed 
intervals. which results in a more complete and consistent set-theoretic 
framework for intervals. which it sounds like JB, at least, may favor.

and as i said earlier, i already have a use case for closed intervals, 
so there's at least one person that needs them. i don't have one for 
open intervals yet, but i suspect there are valid use cases out there.

regards,

al

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