[FOM] Use of AC
Arnon Avron
aa at tau.ac.il
Mon Aug 10 03:17:40 EDT 2009
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
On Sun, Aug 09, 2009 at 01:42:41AM +0100, T.Forster at dpmms.cam.ac.uk wrote:
> I think we are in danger of forgetting that not only do
> most mathematicians-in-the-street not believe AC, most of
> them have no intuitions about it and cannot state it even
> roughly, let alone have any idea how to use it. After all
> most mathematicians are applied mathematicians. Ask yourself:
> how many applied people do i know who can correctly state
> AC? We are a charmed circle!
>
> tf
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