The first obstacle to a student's correct understanding of limits, and the seed of every fundamental misconception about limits, has been the ill-suited language used to express notions of convergence. Near-numbers provide a language suitable for the proper discussion of concepts related to the concept of convergence, allowing us to precisely express ideas that must be clumsily "talked around" when using real numbers alone. Not only do near-numbers provide the symbols through which these ideas an be properly expressed, but they have simple visual representations that open up their every detail to full inspection. These visual representations afford any student who has been introduced to the real line a complete introduction to the topic of limits; moreover, they lead the more advanced student on a natural path to their correct formalization.
The mission of near-numbers is to provide a system that enables a treatment of convergence and limits that is intuitive, precise, unambiguous, and formally accurate, thereby removing all inherent obstacles to a student's understanding.
Specifically, we mean that any misunderstanding, any concept that is troublesome to explain (indeterminacy; the notion of infinity; etc.), should be explicitly resolvable by using the near-number approach. If this goal seems overly ambitious or optimistic, or if some of the benefits of the near-number system seem trivial at first, we encourage a bit of patience and trust; the system has been carefully constructed so as to properly treat every detail of its subject matter, and however small each improvement might seem at first, the net effect on student comprehension can be quite significant. We firmly believe that our goal is achieved through this system, and we will make every effort to demonstrate this to be the case—to this end, questions and/or feedback are emphatically encouraged; we welcome the opportunity to convince both educators and students of this system's value and to promote its use. This site will be freely maintained as central location for resources and discussion regarding the system of near-numbers, available to all of what we hope will become an increasingly large community of proponents.