 It is well-known that coding tricks allow one to do classical mathematics without ever going above cardinality \(c\): for example, the class of all functions from the reals to the reals, is too large to be even a proper class here, but the class of continuous functions is of cardinality \(c\). An individual continuous function \(f\) might seem to be a proper class, but it can be coded as a hereditarily countable set by (for example) letting the countable set of pairs of rationals \(\langle p, q\rangle\) such that \(p \lt f(q)\) code the function \(f\). In fact, it is claimed that most of classical mathematics can be carried out using just natural numbers and sets of natural numbers (second-order arithmetic) or in even weaker systems, so pocket set theory (having the strength of third order arithmetic) can be thought to be rather generous.