Interval arithmetic is neat. This is a great article for introducing modular interval arithmetic too. I'm going to add this to my toy interval arithmetic library when I get a chance. Thanks!

One quirk worth mentioning is equality testing. That is not simply a matter of checking that lower and upper boundaries are equal:

  [4,3] = [8,7]

  [4,4) = [8,8) = (4,4]

(The latter independently of the issue whether you think those sets are empty or the complements of the empty set)