[surrealize]

People have taken different approaches to this in bioinformatics for numbering intervals of dna bases in chromosomes. I think this approach is catching on, though. In that realm, it's important to speak unambiguously about insertions and deletions, and the "interbase" mental model makes it a lot clearer.

edit: Probably the most popular genome browser, based at UC Santa Cruz, uses this zero-based, half-open numbering internally. But, at some point in the past, biologists developed an expectation that numbering would be 1-based. So the Santa Cruz genome browser actually adds 1 to the start position of everything for display purposes.

[rcthompson]

One interesting side-effect of using 1-based closed indexing (i.e. numbering the positions, not between the positions) is that a zero-width range (which is something that actually comes up in genomics) starts at position N and ends at N-1.