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Philosopher Benardete challenged both the conventional wisdom and thereceived mathematical treatment of zero, dot, nine recurring. An initiallypuzzling passage in Benardete on the intelligibility of the continuum revealschallenging 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 vsontology

Analyzing Benardete's comment on decimal notation