²An exception must be made for purely symbolic processing software, such as language compilers. In general, however, heuristic assumptions about what is “correct” already enter by selecting numerical methods that are only guaranteed to be valid with an infinitely dense discretization of the problems at hand, calculating with an infinite machine precision, while one knows in advance that one will in practice, for efficiency reasons, want to stay as far as possible away from these limits. In fact, one often deliberately balances on the edge of “incorrectness” (inaccurate results) to be able to solve problems that would otherwise be too difficult or costly (time-consuming) to solve.