Bolzano’s Infinite Quantities

A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities

A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite...

The Infinite and Infinitesimal Quantities of du Bois-Reymond and their Reception

The mixed fortunes of PAUL DU BOIS-REYMOND'S infinitary calculus and ideal boundary between convergence and divergence are traced from 1870 to 1914. CANTOR, DEDEKIND, PEANO, RUSSELL, PRINGSHEIM and others objected. STOLZ, BOREL, HARDY and others accepted, at least in part, and built further. HAUSDORFF to some extent effected a compromise. The differing attitudes of the different participants to...

N ov 2 00 4 On entropic quantities related to the classical capacity of infinite dimensional quantum channels

Framing of Numerical Quantities

Judgments and decisions are dependent upon the information available. They are also dependent upon the way the information is presented. Message characteristics that make recipients willing to endorse a message have been discussed within the rhetoric tradition and studied empirically in the psychology of persuasion (Cialdini, 2007), advertising (Armstrong, 2010), and health communication (Berry...

Measurements of Electrical Quantities