Comment by jhanschoo

You can look at use cases for an index, and see how well they hold up.

Asking where the smallest greater number (next number) is no longer makes sense.

Taking two numbers and asking whether one is greater than the other still makes sense. (and hence also whether they are equal)

Taking two numbers and asking how far separated from each other still makes sense.

You may already observe some uses for indexes in programming that don't use all of these properties of an index. For example, the index of a hash set "only cares about equality", and "the next index" may be an unfilled address in a hash set.