As announced above, this case study concerns some formal definitions of natural and real numbers and domains of magnitudes, or more precisely of the items that are supposed to recast, within the relevant formal theories, the items that, within informal arithmetic and real analysis we usually call ‘natural numbers’, ‘real numbers’ and ‘magnitudes’. In preparation for this study, some general considerations are in order about different ways to formally define mathematical items forming appropriate domains, as I will say for brevity’s sake, domains of mathematical items.