Abstract—The concept of infinity is analyzed with an objective to establish different infinity levels. It is proposed to distinguish layers of infinity using the diverging functions and series, which transform finite numbers to infinite domain. Hyper-operations of iterated exponentiation establish major orders of infinity. It is proposed to characterize the infinity by three attributes: order, class, and analytic value. In the first order of infinity, the infinity class is assessed based on the “analytic convergence” of the Riemann zeta function. Arithmetic operations in infinity are introduced and the results of the operations are associated with the infinity attributes.

Index Terms—Infinity, class, order, surreal numbers, divergence, zeta function, hyperpower function, tetration, pentation.

Kiamran Radjabli is with Utilicast, La Jolla, California, USA (email: kradjabli@utilicast.com).

Cite: Kiamran Radjabli, "Attributes of Infinity," International Journal of Applied Physics and Mathematics vol. 7, no. 1, pp. 42-48, 2017.