[Om] range & image in fns1
Bruce Miller
bruce.miller at nist.gov
Tue Nov 24 19:32:30 CET 2009
Hi all;
In trying to answer a student's question
about the difference between range and image
(& implicitly codomain) ... and rather stumbling...
Math question:
My naive understanding was that the image is
_exactly_ the set of values produced by a function
over some domain (or subset of the domain)
--- no more, no less.
And, that range is allowed to be some larger set
than the image if it is more convenient for some
purposes (eg continuous, convex, whatever) ...
Is that correct, and are there any formal conditions
on how a range is defined w.r.t an image?
Or is it simply expanded to get whatever desired properties?
OpenMath question:
The description, CMP & FMP for the symbol range at
http://www.openmath.org/cd/fns1.xhtml#range
are contradictory. The description ("range ... merely
required to contain the image") is consistent
with my understanding (such that it is).
However, the CMP says that the range is a subset of
the image, while the FMP goes further saying that
the range is a proper subset (to the extent the
implied "proper" is significant).
Shouldn't the FMP be:
image(f) \subseteq range(f)
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