Augustus de Morgan on divergent series

De Morgan Triples Revisited

In this paper we overview basic known results about the varieties generated by De Morgan triples and about the problem to find equations defining the variety generated by a concrete De Morgan triple. We also provide some alternative proofs and some new results, specially for the case of Łukasiewicz De Morgan triples.

Contact relation on De Morgan algebra

In the paper, the notion of a contact relation on de Morgan algebra is defined, the algebraic structure of all contact relations and the connection to the set of all close, reflexive and symmetric relations on all maximal filters are investigated. 2010 AMS Classification: 06D30, 06F30, 54E05, 54H12

The Morgan Kaufmann Series in

On Absolutely Divergent Series

We show that in the א2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P (ω)/fin. This complements Vojtáš’ result, that under cf(c) = p the two algebras are isomorphic [15].

Neutrix Limit on Divergent Series

In this paper, we give a simple and straight forward definition for the neutrix limit of divergent series and use it to study the neutrix limits of the divergent series ralated to the Rieman-Zeta function ζ(α) and some series related to the polylogarith function Lin(z). Then, we apply the reults to some specific examles. Our reults on Riemann-Zeta function and its derivatives are consistent wit...