NotesFAQContact Us
Collection
Advanced
Search Tips
Back to results
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ887192
Record Type: Journal
Publication Date: 2010-Jul
Pages: 15
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0013-1954
EISSN: N/A
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.
Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://bibliotheek.ehb.be:2189
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A