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In Mathematics, Infinity is not a thing, it is many things. Transfinite arithmetic produces an infinity of infinities! In fact, Infinity opens up so many degrees of freedom that paradoxical behavior seemingly becomes the norm.
This monograph introduces the reader to this fascinating topic and
>A background in High School Algebra and Analytic Geometry will be helpful, as such courses get one used to thinking in such terms. But, really, the only "mathematics" required is some fancy arithmetic and an ability to perhaps visualize 3-D rotations in space. Mostly, thinking logically and rigorously should suffice.
About the author
Rich Coco is a retired "Mathematicaphile", currently residing in the
>After graduating from Woburn High School in May 1970, Rich attended UMass-Amherst that Fall. It was here at UMass that Rich fell hard for both Mathematics and his eventual wife Ida (as fate would have it, in that order). After graduating with a BA-Math degree, Rich was accepted into the Doctorate program (UMass-Amherst) for Mathematics in 1975.
In the summer of 1978, Rich fled the Doctorate program (with a Master's Degree) for a seductive job opportunity at AT&T Bell Laboratories. He always imagined he would continue to pursue his Mathematical interests and finalize his PhD while working. Alas, life, constantly evolving technical direction at work, and an eventual transition into Software Engineering torpedoed any such fantasy.
>As he matured as a Software Engineer, Rich eventually left AT&T and worked at numerous startup companies and Enterprises (eg, Cisco, EMC, Schneider-Electric) as a Principal Engineer or Software Architect and had the good fortune to work across many different technology domains: Network Management, Crypto Security, Video Conferencing, and Tele-Medicine; to name a few.
Through it all, Rich never quite got over his fascination with Mathematics. Now retired, he finally gets to re-engage with it. The intention is to write a series of monographs on special topics for the enthusiastic High School student, introducing him/her to topics, concepts, and ideas that they will not encounter in a standard High School curriculum. Though such topics and fields of endeavor are generally not encountered until one studies Mathematics formally
at the college level, Rich believes many of them can be made accessible and comprehensible to an interested and motivated High School student. In this way, the student will get a glimpse into the extraordinary breadth, depth, and beauty of the field of study referred to as Mathematics. This will be a perspective that is inaccessible in the standard test-driven High School Mathematics curriculum.
