It is the standard construction of the natural numbers in set theory, known as von Neumann ordinals. If what you're doing is otherwise set-theoretic, you can use it (but it would still me merciful towards your readers to remind them of how it works, unless there are ordinals everywhere). Otherwise the conception of a natural number as the set of the numbers that come earlier is generally supposed to be an "implementation detail" that one should not have to think of when using the naturals.
Rule of thumb: If it makes sense in your context to consider the naturals defined by the Peano axioms rather than set theoretically, don't assume that your reader will be prepared to consider them sets.
Any particular reason not just to write $0\le i<n$?