[FOM] Q and A

Gabriel Stolzenberg gstolzen at math.bu.edu
Tue Nov 6 21:25:40 EST 2007

   Question.  What is the name of the famous conjecture in analysis
whose proof by Abraham Robinson is sometimes offered as a demonstration
of the power of nonstandard analysis?  (Jim Holt did this in the NYR
but, as I recall, without identifying the conjecture.)

   Answer (to a different question).  In response to a posting several
months ago asking to see applications of the Baire Category Theorem,
"A Primer of Real Functions" by Boas & Boas, is advertised as having 10
of them, one of which, almost surely, is the striking fact that "most"
continuous functions on [0,1] are nowhere differentiable.  (E.g., the
set of continuous functions on [0,1] that are differentiable at at least
one point is a countable union of nowhere dense sets.)

   Gabriel Stolzenberg

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