Limits and the system of near-numbers

Details Limits and the system of near-numbers Limits and the system of near-numbers

2004-12-08

arxiv.org/abs/math/0412157v1

Mathematics

General Mathematics

19 pages; in the process of submission

Scientific paper

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.

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