ERIC Number: EJ887192
Record Type: Journal
Publication Date: 2010-Jul
Abstractor: As Provided
Reference Count: 0
Zooming in on Infinitesimal 1-.9.. in a Post-Triumvirate Era
Katz, Karin Usadi; Katz, Mikhail G.
Educational Studies in Mathematics, v74 n3 p259-273 Jul 2010
The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity. We discuss the key ideas about infinitesimals via a proceptual analysis of the meaning of the ellipsis "..." in the real formula 0.999... = 1. Infinitesimal-enriched number systems accommodate quantities in the half-open interval [0,1) whose extended decimal expansion starts with an unlimited number of repeated digits 9. Do such quantities pose a challenge to the unital evaluation of the symbol "0.999..."? We present some non-standard thoughts on the ambiguity of the ellipsis in the context of the cognitive concept of "generic limit" of B. Cornu and D. Tall. We analyze the vigorous debates among mathematicians concerning the idea of infinitesimals.
Descriptors: Number Systems, Epistemology, Mathematics Education, Evaluation, Intervals, Mathematical Formulas, Arithmetic, Mathematics, Professional Personnel, Numbers
Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: email@example.com; Web site: http://www.springerlink.com
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Authoring Institution: N/A