Welcome to my Eagle Ridge Academy (ERA) Math Teams site!
Here you will find information for both the School of Logic (SoL) Math Team (for grades 6-8) and the School of Rhetoric (SoR) Math Team (for grades 9-12), as well as a wide selection of fun and helpful mathematics resources. You can navigate about the site using the menu at the top of each page.
I hope you enjoy continued visits to 0islessthan1.weebly.com. Got a question, comment, concern, or suggestion? Email me, Mr. Stephen MacLennan, ERA SoL Math Team Coach & SoR Math Team Coach, at [email protected].
Why "0 is less than 1"?
The story of why the URL of this site, www.0islessthan1.weebly.com, includes the phrase 0 is less than 1 may be traced to a time when I was an undergraduate mathematics (and electrical engineering) major at the University of Minnesota in Minneapolis. My brother Don telephoned me and asked what I had done that day. I was then taking a course entitled Fundamentals of Algebra, which addressed the algebraic topics of group theory, ring theory, and field theory, useful among other things in providing the basis for the definition and construction of number systems, with applications to digital communication, cryptography, and more. I informed Don that I had in fact just proved that 0 is less than 1.
Rather bemused, Don wondered why the proof of such an obvious fact would be necessary. I explained how the "facts" of mathematics - even "obvious" ones - are determined via proof using deductive reasoning from a small number of accepted self-evident postulates that are assumed to be true and selected facts (aka theorems) that we have previously proved to be true. (An example, of a postulate is that which states an additive identity exists: a + 0 = 0 + a = a, namely, that adding 0 to a number leaves the number unchanged.). Some facts indeed appear obvious to us because we are now so familiar with them and are convinced of their veracity and applicability, yet as one proves more and more facts in a disciplined, mathematical manner, one finds some facts are quite unexpected. (For example, that the square root of 2 is irrational, which initially freaked out the ancient Greeks so much they tried to keep it secret.) Yet what these facts all share is their truth, given the assumed truth of the original small number of postulates, exemplifying the principle that from small things, great things come.
Even now, decades later, Don will often introduce me to others, saying, "This is my younger brother Stephen. He can prove that 0 is less than 1." Rest assured that at social gatherings I refrain from scattering those present by plunging headlong into an actual proof, but, surprisingly enough, this introduction has served rather well as a lighthearted conversation-starter.