For as long as there have been theories of arbitrary objects, many of the paradigmatic examples of arbitrary objects have been drawn from number theory (arbitrary natural numbers, for instance) and geometry (arbitrary triangles, for instance). In this chapter, I take a closer look at some examples of arbitrary objects that are related to number theory. In particular, I investigate the properties of arbitrary natural numbers and the epistemological importance of arbitrary finite strings of strokes, which can play the role of natural numbers, as Hilbert taught us more than a century ago.