Re: ONE


fernando revilla wrote:
> > In reality that's a good explanation. But it renders
> > the meaning of One
> > non mathematical !
> > or more appropriately speaking prior to mathematics
> > and perhaps even to
> > logics, it makes it a completely intuitive concept in
> > reflection to
> > percepts.
>
> I meant "one" as a primitive concept i.e. as thinking or fixing the mind
> in an entity as a whole. But in mathematics we need to extract in an exact
> way the substance in the context we are dealing with ( see the first post
> of Abraham ), "one" as cardinal, "one" as ordinal, "one" as identity element
> in a group,in a field,...

I agree with you about the primitive concept, yet this concept can be
extracted into a one stem that can be expressed in a pre mathemactical
language like the quality break I demonstrated , and this stem can then
branch into one as cardinal, as ordinal as identity etc........ . All
of what I am saying is that there is a common concept between all these
one, which is the Stem one , and that stem one can be expressed in a
premathematical
exact manner . So what we have is the following:

Perception -> Intuitive primitive concept -> exactly defined Stem One
-> Applied One to
various field of Cardinality, ordinality, identity, peculiarity,.......

It is obvious that Stem One is related to the difficult unsolved issue
of The Whole and The Part. I think that these concepts are prior to
the concept of number , they are related
to the concept of quantity versus quality.

I think that my definition of Stem One as the domain of incomplete
subtraction that acheives quality break , is important definition for
understanding One. It is what you call
necessary definition One.

Zuhair



>
> > Yet I think my atomic explanation of the meaning of
> > One is more
> > appropriate.
> >
> > One is were quality breaks.
> >
> > An illiterate man had a group of checkin, and a
> > clever theif used to
> > steel his checkins in such a manner that at least one
> > checkin should be
> > left,however one day the theif was so hungery that he
> > cut the only left
> > checkin into two halfs , and took one half.
> >
> > at that stage the illiterate owner knew that he was
> > rubbed.
> >
> > what I mean if we define a process of what I call "
> > Incomplete
> > subtraction" symbolized
> >
> > as -'
> >
> > Now a -' b = c -> c>0
> >
> > Let denote a as the domain of -' and b the codomain
> > of -'
> >
> > So dom( -' ) in a -' b = a
> >
> > and codom( -' ) in a-' b = b
> >
> > Now if I have a group of a let me symbolize it as
> > Ua
> >
> > so Ua can be aaa or aaaa or a or any repeatition of a
> >
> > Now suppose we don't know how to count so if we see
> > aaa we symbolize
> > it as Ua
> >
> > and if we see aaaaa we symbolize it as Ua
> >
> > Now : Ua -' Ua =' Ua -> dom ( -' ) in Ua -' Ua = Ua
> > is not One a.
> >
> > =' means there is a possibility to "lead to" .
> >
> > Ua -' Ua =/=' Ua -> dom ( -' ) in Ua - Ua =/= Ua
> > Ua is One a.
> >
> > =/=' means not possible to "lead to" at all.
> >
> > for example I can have 5 checkins and I can steel 4.5
> > checkins, what
> > remains is 0.5 checkin which is not a checkin , yet
> > that doesn't lead
> > to 5 equalling one.
> >
> > because it is possible to subtract 4 from 5 and what
> > remain is one
> > checkin which is checkin. or 3 from 5 and what
> > remains is 2 checkin
> > which is checkin more precisely
> > Ucheckin.
> >
> > while if we have one checkin as the domain of
> > operation -' , then it is
> > not possible
> > to be left with U checkin , we will always have a
> > part of a checkin and
> > not a checkin
> >
> > that is what I call type or quality break.
> >
> > Any comment?
> >
> > Zuhair
>
> Yes, you have selected "one" point ( better "a" point ) in the continuum.
>
> Definition. ZERO=CAT , ONE=DOG
>
> This is a very good definition if we suppose
>
> i) CAT is not a successor in the sense of PA.
> ii) DOG is the successor of CAT in the sense of PA.
>
> I think you are looking for a non necessary quality of ONE ( or should
> I say a necessary definition of ONE )
>
> Fernando.

.

Quantcast