On the Subrecursive Computability of Several Famous Constants

Abstract: for any class f of total functions in the set n of the natural numbers, we define the notion of f-computable real number. a real number α is called f- computable if there exist one-argument functions f, g and h in f such that for any n in n the distance between the rational number f(n) . g(n)over h(n)+1 and the number α is not greater than the reciprocal of n + 1. most concrete real numbers playing a role in analysis can be easily shown to be ε3-computable (as usually, em denotes the m-th grzegorczyk class). although (as it is proved in section 5 of this paper) there exist ε3-computable real numbers that are not ε2-computable, we prove that π, e and other remarkable real numbers are ε2-computable (the number π proves to be even l-computable, where l is the class of skolem’s lower elementary functions). however, only the rational numbers would turn out to be ε2-computable according to a definition of f-computability using 2n instead of n +1.