Re: Review of Mueckenheims book.

On Mar 9, 12:19 pm, David Marcus <DavidMar...@xxxxxxxxxxxxxx> wrote:
MoeBlee wrote:
On Mar 9, 9:42 am, David Marcus <DavidMar...@xxxxxxxxxxxxxx> wrote:

and it's widespread in basic mathematics;

Nonsense.

No, it is. I didn't say it is dominant, the majority. But it is
widespread. You can find it in a wide variety of books on general
mathematics.

I've looked, and I can't.

Of course not, you even take even HALMOS to be saying that the
function itself is a triple no matter that he says it is a RELATION.

and it is consistent with other basic mathematical terminology;

Nonsense.

I showed it. You just dogmatically grunt, "nonsense".

The standard definition is more consistent.

It's nearly inconceivable to put that to a test, going through
thousands upon thousands of books and articles, with all kinds of
terminology flying around, to compare which of two different
formalizations adhere to more of the text than the other.

If you prefer your formalization, then FINE. I have NO ARGUMENT with
you using it. But it's just not anywhere CLOSE to being a standard
that a function is a triple.

Standard
terminology in basic abstract algebra, analysis, and (first
sememester) topology?

Exactly.

The function f ITSELF as a triple?

Exactly.

Please cite.

Already did, but apparently you don't know how to read normal math
books.

Thank you for that incompetently snide insult.

Merely a statement of fact.

It's a sophomoric ill-premised insult.

And you claim that that *I* don't know how to read a textbook when YOU
claim that Halmos considers a function to be triple! You're a riot.

No crime to make a mistake, but to insist
that you are right when the mistake is pointed out...

No, you just want me to take YOUR INTERPOLATION toward a formalization
as if it is a standard when it is not, as DEMONSTRATED. But how could
you follow very much given that you KEEP INSISTING that Halmos thinks
of a triple even when he WRITES "a RELATION" [emphasis added].

Halmos is pretty clear, but somehow you managed to misinterpret
what he wrote as support for your position.

Now you've really overstepped. Halmos says a function is a triple?!!!
No, Halmos says a function is a certain kind of RELATION. Go back and
read:

"A function from X (or on) X to (or into) Y is a RELATION [...]:
[emphasis added]
And look at page 48 where he gives a TEST for functionhood, which is
not that a funciton is a certain kind of triple, but rather that a
function is a certain kind of relation.
Wow, you really are imperious! You directly contradict Halmos to claim
that he is adopting YOUR approach when it is EXPLICT that he is not.

The "to Y" is part of the definition.

Yes, and the definition may just as easily be understood to be of a
three-place relation among u, X and Y as it may be ERRONEOUSLY crammed
into defining a triple.

The definition has CONJUNCTS:

One of those conjucts IS that u is a RELATION.

There other conjuncts are as to X and as to Y.

And the definition then describes a relation among the function, its
domain, and a codomain.

And Halmos MAKES EXPLCIT that the TEST for u itself being a function
is whether or not u is a RELATION such that; he says THAT, and he does
NOT say that u is a TRIPLE/

When Halmos, more than once, says the function is a relation, then I
think we can take him to really mean that the function IS a relation.

MoeBlee

.

Relevant Pages

  • Re: Review of Mueckenheims book.
    ... You can find it in a wide variety of books on general ... The standard definition is more consistent. ... that you are right when the mistake is pointed out... ... Halmos says a function is a certain kind of RELATION. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... You can find it in a wide variety of books on general ... Halmos says a function is a certain kind of RELATION. ... assess all the different kinds of terminology people use orally. ... Like you "UNDERSTAND" Halmos to be saying that a function is a ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... by books such as Hocking & Young). ... Your INTREPRETATION is not standard in general mathematics. ... I'm proposing a formalization so that ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... Yes, in general, we can have a 'function is a triples' formalization, ... AND we can ALSO have a three-place predicate formalization, ... triples formalization does NOT fit Halmos in particular, ... Why don't you just respond to the fact that Halmos is explicit that a ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... is your chance just to think and see that Halmos says a "relation" NOT ... relation and he doesn't say it's a triple, so my formalization may not ... is quite in keeping with ordinary set theory, ... domain, codomain, and set of ordered pairs such that etc. ...
    (sci.math)