Asymptotes - Frustrating Problems With Unsatisfying Solutions.
Image via Wikipedia In our last posting, we discussed the notion of asymptotes , and I posed two problems for your consideration. One involved the eventual (but unreachable) sum of a convergent series of numbers, and the other involving a ever-more troubling fraction. You can quickly refresh your memory by clicking on http://braintenance.blogspot.com/2011/09/asymptotes-closer-but-never.html , and by then hitting your browser's "BACK" button. The answers are unsatisfying, but they were promised: 1) In adding the sum of the series 1 + 1/2 + 1/4 + 1/8....and so forth, the sum will eventually approach, but never quite reach a limit of 2. 2) In dividing (n-1)/n, as n increases, the value of the expression approaches, but never reaches 1. There are examples of this type of complex conundrum in nature, in such things as trying to solve 22/7 (which is a never-ending decimal), and in determining the halflives of certain radioactive materials (isotopes), where one half of the ma...