2004/12/08 by Frank Swenton, Swenton, Frank
Mathematics · #Mathematical and Theoretical Analysis #math.GM
paper · pdf · doi:10.48550/arxiv.math/0412157
19 pages; in the process of submission
arxiv created 2004/12/08 · arxiv updated 2009/12/01
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers properly fit the context of limits, allowing precise and unambiguous notation in limit computation. More importantly, the near-numbers are a set of concrete mathematical objects that provide a scaffold both for building an accurate intuitive understanding of the limit concept and for connecting that understanding to the formal definition of the limit.