9 citations · 24 across the 19 of their papers we have counts for
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Back to Classics: Teaching Limits Through Infinitesimals
Todor D. Todorov
The usual -definition of the limit of a function (whether presented at a rigorous or an intuitive level) requires a "candidate " for the limit value. Thus, we have to start…
Completeness of the Leibniz Field and Rigorousness of Infinitesimal Calculus
James F. Hall, Todor D. Todorov
We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of ten equivalent statements} borrowed from algebra, real analysis,…
Nonstandard Analysis in Topology
Sergio Salbany, Todor Todorov
We present Nonstandard Analysis by three axioms: the {\em Extension, Transfer and Saturation Principles} in the framework of the superstructure of a given infinite set. We also pre…
Stochastic Homology. Reduction Formulas for Computing Stochastic Betti Numbers of Maximal Random Complexes with Discrete Probabilities. Computation and Applications
Todor Todorov
Given a chain complex with the only modification that each cell of the complex has a probability distribution assigned. We will call this complex - a random complex and what should…
Another Proof of the Existence a Dedekind Complete Totally Ordered Field
James F. Hall, Todor D. Todorov
We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to another construction of a Dedekind complete totally ordered field or, equivalently…
An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms
Todor D. Todorov
We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sen…