Zooming in on Infinitesimal 1-.9.. in a Post-Triumvirate Era

Autor/inn/en	Katz, Karin Usadi; Katz, Mikhail G.
Titel	Zooming in on Infinitesimal 1-.9.. in a Post-Triumvirate Era
Quelle	In: Educational Studies in Mathematics, 74 (2010) 3, S.259-273 (15 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-010-9239-4
Schlagwörter	Number Systems; Epistemology; Mathematics Education; Evaluation; Intervals; Mathematical Formulas; Arithmetic; Professional Personnel; Numbers + Suchen Sie Ihr Suchwort? Number system; Zahlensystem; Erkenntnistheorie; Mathematische Bildung; Evaluierung; Mathematische Formel; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Personalbestand; Zahlenraum
Abstract	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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10