 This section has given just an introductory taste of the mathematics of ordinal and cardinal numbers—it has come to be called Cantor’s Paradise. But we have already seen many characteristic features of these notions of infinity that differentiate them starkly from those discussed in the previous section. Just as the differences between the natural numbers and the real numbers demonstrate the differences between counting elements of sets, and measuring lengths, areas, and so on, the differences between Cantor’s cardinals and the extended reals further demonstrate differences between counting and measuring.