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Author: Jason Hathcock

Sequences & Tendency: Topology Basics Pt. 2

Sequences & Tendency: Topology Basics Pt. 2

Introduction In my previous post I presented abstract topological spaces by way of two special characteristics. These properties are enough to endow a given set with vast possibilities for analysis. Fundamental to mathematical analysis of all kinds (real, complex, functional, etc.) is the sequence. We have covered the concept of sequences in some of our…

Building a Ground Floor: Topology Basics Pt. 1

Building a Ground Floor: Topology Basics Pt. 1

Like some other terms in mathematics ("algebra" comes to mind), topology is both a discipline and a mathematical object. Moreover like algebra, topology as a subject of study is at heart an artful mathematical branch devoted to generalizing existing structures like the field of real numbers for their most convenient properties. It is also a…

Carnival of Mathematics 154

Carnival of Mathematics 154

The Math Citadel is happy to host Carnival of Mathematics edition , where we take a look at math blog posts from all around. For all those interested in Carnival of Mathematics future and past, visit The Aperiodical. Observing Tradition To get things started, we present a few interesting properties of , in keeping with Carnival…

All the Same Opposites

All the Same Opposites

Editor's note: see this appendix for supporting proofs. Fields are among the most convenient algebraic structures, preserving much of the arithmetic we know and love from familiar fields like the rationals and the real numbers . Now, it is unnecessary that a set possess infinitely many elements to possibly constitute a field (under the right…

Extensions of the Single Server Efficiency Model

Extensions of the Single Server Efficiency Model

For the full paper, which includes all proofs, click here. Abstract Editor's note: this paper comprises the third chapter of the PhD dissertation by Rachel Traylor. Visit here and here to see chapters one and two, respectively. Herein we further generalize the single server model presented in [3]. In particular, we consider a multichannel server…

A Note on Russell’s Paradox

A Note on Russell’s Paradox

Topics in mathematics very frequently rely on set theory (I am hard-pressed to quickly think of one that doesn't). Set theory itself is a very abstract area of study. Even so, mathematicians built it on axioms (self-evident truths taken as fundamental starting points), and, of course, debate continues to this day as to which axioms…