An application of surreal numbers to the asymptotic analysis of certain exponential functions
An application of surreal numbers to the asymptotic analysis of certain exponential functions
Skolem (1956) studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant 1, the identity function x, and such that whenever f and g are in the set, f+g, fg and f^g are also in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz (1984) computed the order type of the fragment below 2^(2^x). They did so by studying the possible limits at infinity of […]