Re: Review of Mueckenheims book.

On Mar 8, 7:02 pm, David Marcus <DavidMar...@xxxxxxxxxxxxxx> wrote:
MoeBlee wrote:
On Mar 8, 1:54 pm, Virgil <vir...@xxxxxxxxxxx> wrote:

Definition: If f = (X,Y,S) is a function, then the codomain of f is Y.

So, AGAIN, what is your definition of 'codomain' now?

Marcus' definition works for me.- Hide quoted text -

I'm all for talking about a triple <D C f> where f:D->C.

But then the function is f and the triple is not the function.

We say things like "Let f be a function" or "Let f be a function from
D into C". We don't say "Let <D C f> be a function" or "Let <D C F> be
a function from D into C".

People who write carefully say f: X -> Y is a function.

And people who interpret carefully may as easily understand that that
rolls off the tongue but, in garden variety math, it may be taken as
(and is actually more rigourously taken as): f is a function & domain
of f is X & the range of f is a subset of Y. All we really

If X and Y are
understood from the context, people may not mention them.

And some people also say "f is function" and may not be specifying any
particular subset of the range of f. To prove 'f is a function' it
suffices to prove that f is a relation of a certain kind. Simply to
prove that f is a function does not also require proving that it has a
certain specified superset of its range.

'f is a function from D into C' is a statment about a relation among
f, D, and C - a relation among the function f, the domain of f, and a
superset of the range of f.

'f is a function' is a statement about f.

f is the function.

Get used to it.

You are welcome to your personal preferences, but this isn't the
standard usage.

It's standard in set theory; and it's widespread in basic mathematics;
and it is consistent with other basic mathematical terminology; and my
definition of the one-place 'f is a function' follows right from such
definitions as you posted from textbooks, as I proved.

Now, YOUR f = <D C S> is found where as standard terminology? Standard
terminology in basic abstract algebra, analysis, and (first
sememester) topology? The function f ITSELF as a triple? Please cite.

I have the impression that you've learned most of your mathematics from
books. Is that correct?

Oh, if you want to say that what goes on orally in classrooms in front
of chalkboards is often a lot different from what goes on in books,
then I have no dispute about that. My gosh, I could not possibly
assess all the different kinds of terminology people use orally.

MoeBlee

.

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