[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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