01/06/2011, 01:14 AM
I see potential in this approach because the hyperreal number system is easier to work with than the real numbers when performing analysis. With the hyperreals, problems in Calculus become expressible in terms of logic and abstract algebra.
The analytic continuation of tetration and its inverse-operations may seem more forthcoming when using this approach. It may even be possible to identify certain properties that make the continuation unique (ie: Logarithmic Convexity was used to analytically continue the factorial via the construction of the Gamma Function, which is a unique continuation).
The analytic continuation of tetration and its inverse-operations may seem more forthcoming when using this approach. It may even be possible to identify certain properties that make the continuation unique (ie: Logarithmic Convexity was used to analytically continue the factorial via the construction of the Gamma Function, which is a unique continuation).