[FOM] Use of AC
T.Forster at dpmms.cam.ac.uk
Mon Aug 10 17:49:41 EDT 2009
This is spiralling out of control, so this will be my last post. Implicit
use of AC is everywhere, of course. What is not everywhere is the kind of
understanding of AC that FOM listmembers have. Arnon's illustration is a
good one. I ask: how many of the people who learn this fact as u/gs can
identify and explain the use of DC in its proof? Precious few, i bet.
Our preoccupations and concerns (as instance Freiling's argument) are
not shared by most people who are considered mathematicians.
On Mon, 10
Aug 2009, Arnon Avron wrote:
> AC (at least in the weaker form of DC) is implicitly
> used in any first course in analysis (as given e.g. at
> all universities in Israel to first-year students
> of mathematics). Thus it is used for proving the equivalence
> of the two definitions of continuity: the \delta-\espsilon
> one, and the one that uses sequences. Someone who does
> not know such basic material cannot be called
> "a mathematician" (neither in the street nor anywhere else).
> Arnon Avron
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