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 <i>not</i> simply a matter of checking that lower and upper boundaries are equal:<p><pre><code> [4,3] = [8,7]
[4,4) = [8,8) = (4,4]
</code></pre>
(The latter independently of the issue whether you think those sets are empty or the complements of the empty set)