Re: Review of Mueckenheims book.

On Mar 2, 7:09 pm, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1172858408.942752.235...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"MoeBlee" <jazzm...@xxxxxxxxxxx> wrote:
The range of a function is usually defined as the set of all values that
the fuction takes,

Right, but the definition may be more general, so that it is not just
for functions or even relations:

range(s) = {y | Ex <x y>es}

and can be a proper subest of the codomain, which is
merely a set in which all those values lie but which may contain other
members which are not values of the function.

Right, that is how many authors use 'codomain'. And since there is not
a unique codomain, I don't use the expresssion 'THE codomain'.

See domain, range and codomain as explained inhttp://en.wikipedia.org/wiki/Function_%28mathematics%29

or seehttp://mathworld.wolfram.com/Codomain.html

Oh, come on, Virgil, as to the extent that that is addressed to me, I
really don't need that. I don't get my definitions from WIKIPEDIA, for
godssakes or usually from other Internet sites, but rather from good
textbooks. If I do consult an Internet site for a definition, I'll use
the Springer encyclopedia online.

For those accustomed to dealing mostly with real functions, as in
calculus, distinguishing between functions which have the same domain
and and range but differing codomains may seem excessively picky, but
there are areas, e.g., category theory, in which it is important.

Okay. And there's nothing I posted about this that fails to hold up to
whatever pickiness you want to apply.

MoeBlee

.

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