Mykel Alvis wrote: > > Actually, I refute the existence of the [9:00,9:00) interval, if it is > defined in accordance with the general set definitions as I understand them > and as we seem to agree that they are definied. To clarify: > 1. the square bracket is INCLUSIVE > 2. the parenthesis is EXCLUSIVE > therefore, the interval [9:00,9:00) is both inclusive (on the left) and > exclusive (on the right) and is therefore nonsensical. >
>> On 7/6/06, Nils Kilden-Pedersen <[EMAIL PROTECTED]> wrote: >> > >> > I believe [ is inclusive, ) is exclusive, so [9:00, 9:00) would be >> > [9:00, 8:59:999999999999999999] which does not make sense. >> > i sort of made a similar point in one of my posts, so let me outline my own clarified thinking on this. the normal interval notation [x, y) _requires_ that x <= y and _defines_ the _set_ of all numbers z that lie between x [INCLUSIVE => x <= z] and y [EXCLUSIVE => z < y]. according to the rules, the zero-length half-open interval [x, x) _is_ a meaningful entity (because x <= x) but the _set_ that it defines is empty. several people (including stephen) have argued that we should just use the rules relating to empty sets. in this view, all zero-length intervals [x, x) are identical to the empty interval. i've argued that if we use this interpretation, we should just use a special value that represents an empty interval that returns null (or the equivalent) when queried for its end points. my only caveat is that we keep in mind for future reference that the zero length _closed_ interval _is not_ empty. i.e. we shouldn't embed into code the assumption that the zero-length interval is empty. i (and stephen) have also argued that it's non-intuitive to lose the information on end points when the zero-length interval is being constructed. however, this depends very much on the use that is made of such an interval. if we do decide that the end-points of the zero-length interval are meaningful, there's nothing stopping us from adding an additional rule (3) to the standard definition of the interval. i.e. [x, x) is the set that is the limit of the sequence of sets [x, x + epsilon) as epsilon approaches zero. note that we could use an alternative rule (3a) i.e. [x, x) is the set that is the limit of the sequence of sets [x - epsilon, x) where we now approximate the interval increasingly closely from the left. this rule will give a different set of results for operations involving zero length intervals. whether we should use the unmodified interval definition or one with added rules depends on how the zero-length intervals wind up getting used. at this point, i've argued on all sides of this issue, because they all have merit. which implementation Stephen decides to go with should be dictated (as it usually is when Stephen makes the final call) by the actual use cases. so probably the most important question is (and again several people have mentioned this) what are the ways in which these intervals are actually being constructed / used? regards, al Using Tomcat but need to do more? Need to support web services, security? Get stuff done quickly with pre-integrated technology to make your job easier Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo http://sel.as-us.falkag.net/sel?cmd=lnk&kid=120709&bid=263057&dat=121642 _______________________________________________ Joda-interest mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/joda-interest
