Limits and the system of near-numbers Export

@misc{citeulike:3324, abstract = {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.}, archivePrefix = {arXiv}, author = {Swenton, Frank}, citeulike-article-id = {3324}, citeulike-linkout-0 = {http://arxiv.org/abs/math.GM/0412157}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.GM/0412157}, day = {8}, eprint = {math.GM/0412157}, keywords = {learning, math}, month = {December}, posted-at = {2004-12-11 07:44:09}, title = {Limits and the system of near-numbers}, url = {http://arxiv.org/abs/math.GM/0412157}, year = {2004} }

TY - ELEC ID - citeulike:3324 L3 - citeulike-article-id:3324 N2 - 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. TI - Limits and the system of near-numbers KW - learning KW - math AU - Swenton, Frank PY - 2004/12/08/ UR - http://arxiv.org/abs/math.GM/0412157 ER -