This paper deals with the so-called ``black-box testing'' for stateless systems (upon the same input, a stateless system always produces the same output). A large number of practical systems is stateless, including combinatorical circuits and numerical software or hardware systems. Only numerical systems testing is considered. Since finite testing is inherently inconclusive, the authors modify the usual problem in three different directions (an infinite sequence of tests for which the testing is decidable in the limit; relaxation of the error criterion; tolerance of faults on a negligible subset of inputs) and obtains positive results which indicate that test sets are universal. They only depend on the structure of the input set and they are provided by an \(\varepsilon\) net of the input set.