Nonstandard Analysis A Practical Guide with Applications
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881
Robert Lutz Michel Goze
Nonstandard Analysis A Practical Guide with Applications
Springer-Verlag Berlin Heidelberg New York 1981
Authors
Robert Lutz Michel Goze Institut des Sciences Exactes et Appliquees, Universite de Haute Alsace 4, rue des Freres l.umiere, 68093 Mulhouse - Cedex, France
AMS Subject Classifications (1980): 03 Hxx, 34 Exx
ISBN 3-540-10879-3 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-10879-3 Springer-Verlag New York Heidelberg Berlin
CIP-Kurztitelaufnahme der Deutschen Bibliothek Lutz, Robert: Nonstandard analysis: a pract. guide with applications 1 Robert Lutz; Michel Goze.Berlin; Heidelberg; New York: Springer, 1981. (Lecture notes in mathematics; Vol. 881) ISBN 3-540-10879-3 (Berlin, Heidelberg, New York) ISBN 0-387-10879-3 (New York, Heidelberg, Berlin) NE: Goze, Michel:; GT This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1981. Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
Dialogue
On the University's premises,
- Are you familiar with the non-standard methods ? ???
- Non-standard Analysis, if you prefer I I ve
heard
about
Infinitesimals
and
the
like,
that
seem to be
coming back into fashion. But why call it a method? Because into
it's
not
fashion,
so
but
much
a
rather
question
of
of
bringing
furnishing
a
new
infinitesimals
proving
tool,
a
non-standard one for those unfamiliar with it. Do you intend to modify our standards
of
reasoning ? You would' nt
be the first ... But old math is good enough for me ! Not".
at
all
objects trick ever
The
non-standard
infinitesimals,
of language, asymptotic
for
method.
instance -
introduces
intermedi ate
by means of a very simple
in order to simplify the proofs
behaviours
are
concerned
mainly when-
and to make them close
to heuristic approaches. But
you
the
add something
frame
that
so
your
as
the
It's no
introduce
reasoning
Undoubtedly to
to
becomes
one
So, to
there
non
is
search
prove
nothing
classical for
known
new
proof,
the
is
or
But
is
is
classical
Enlarging
want it
no still
strictly
wonder
valid
?
equivalent
reasoning
about
the
equivalent to a classical one. in
there
latter.
results
non
same math
you
mathematics
every
usual mathematical objects a
simpler
Non-standard
standard
longer the
everything
your is
Your
method
also
a
method
you produce a
Because classical
is
pointless
if
one.
you I
have
o'-'efer
either
you
new result that you could,
after all, prove in another way. What's the gain? Your
are
one
of
those
who
prefer
of t
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