The set of computable integer sequences is countable. The preimage of a recursive set under a total computable function is a recursive set. Moreover, the equality of two computable numbers is an undecidable problem. Computational complexity theory deals with the relative computational difficulty of computable functions. Some constructivists accept the existence of only those reals that are computable. The list of undecidable problems gives additional examples of problems with no computable solution. The image of a computable set under a total computable bijection is computable. The set of computable numbers has the same cardinality as the natural numbers. Discrete logarithms are quickly computable in a few special cases. It cannot compute everything that is computable. In mathematics, "effective" is sometimes used as a synonym of "algorithmically computable". The only assumption is that the environment follows some unknown but computable probability distribution. Let formula 3 be an admissible numbering of the computable functions. This difficulty is addressed by considering only sequences which have a computable modulus of convergence. This has led to the study of the computable numbers, first introduced by Alan Turing.