 In the first two classes of system discussed in this section, logical considerations lead to the construction of theories in which “familiar” parts of the world look quite different. Constructive mathematicians do not see the same continuum that we do, and if they are willing to venture into the higher reaches of set theory, they find a different world there, too. The proponents of nonstandard analysis also find it useful to look at a different continuum (and even different natural numbers) though they do see the usual continuum and natural numbers embedded therein.