ANALYZING BENARDETE`S COMMENT ON DECIMAL NOTATION

JACQUES BAIR, PIOTR B LASZCZYK, KARIN U. KATZ, MIKHAIL G. KATZ, TARAS KUDRYK, AND DAVID SHERRY

【摘要】哲学家贝纳德特挑战了传统的智慧和公认的的数学处理的0.999……。贝纳德特关于连续统可理解性的一段最初令人费解的文字，揭示了对数系、现代分析基础和数学教育的富有挑战性的见解。这里的一个关键概念，用陶的术语来说，就是“超极限”。

关键词：实分析；无穷小；十进制表示法；过程与本体

Abstract. Philosopher Benardete challenged both the conventional wisdom and the received mathematical treatment of zero, dot, nine recurring. An initially puzzling passage in Benardete on the intelligibility of the continuum reveals challenging insights into number systems, the foundations of modern analysis, and mathematics education. A key concept here is, in Terry Tao`s terminology, that of an ultralimit.

Keywords: real analysis; infinitesimals; decimal notation; procedures vs ontology

at journal​socialsciences.exeter.ac.ukAnalyzing Benardete's comment on decimal notation​arxiv.org