Re: Unusual terminology: "correspondence"
- From: "Ignacio Larrosa Caņestro" <ilarrosaQUITARMAYUSCULAS@xxxxxxxxxxx>
- Date: Fri, 14 Oct 2005 18:52:45 +0200
En el mensaje:h6G3f.10181$Hm3.8831@xxxxxxxx,
Stephen J. Herschkorn <sjherschko@xxxxxxxxxxxx> escribió:
> This evening I was tutoring a client who was having difficulty with
> her graduate-level "Mathematics for Microeconomics" course. Her
> instructor introduced the following terminolgy: A *correspondence*
> from a set X to a set Y is by definition a function from X to P(Y)
> (the power set). Furthermore, he consistently used the
> notation p: X -> Y to denote correspondences as well as functions.
> He would distinguish between the two by stating explcitly which it
> was and by generally using a lower-case Greek phi for correspondences
> and an f for functions.
> I find the notation deplorable, and I have never come across this
> definition before. The material is highly mathematical, with much
> discussion of general metric spaces. Are this terminology and
> notation common in the microeconmics literature, or are they peculiar
> to the instructor?
I think that is standard. A 'correspondence' between sets A and B is a
subset of the product set A*B. Also called, depending on the context, as a
'relation'.
A function is then an univoque correspondence, a correspondence from 'many'
(one or more) to 'one', instead a general correspondence, that is 'many' to
'many'.
--
Saludos,
Ignacio Larrosa Cañestro
A Coruña (España)
ilarrosaQUITARMAYUSCULAS@xxxxxxxxxxx
.
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