Re: Understanding the quotient ring nomenclature

On Jun 24, 11:43 am, Tonico <Tonic...@xxxxxxxxx> wrote:
On Jun 24, 4:34 pm, "Tim BandTech.com" <tttppp...@xxxxxxxxx> wrote:



On Jun 23, 5:13 pm, Arturo Magidin <magi...@xxxxxxxxxxxxxx> wrote:

On Jun 23, 4:03 pm, "Tim BandTech.com" <tttppp...@xxxxxxxxx> wrote:

On Jun 23, 1:22 pm, Leland McInnes <leland.mcin...@xxxxxxxxx> wrote:

On Jun 23, 9:03 am, "Tim BandTech.com" <tttppp...@xxxxxxxxx> wrote:

I'm sorry Leland but this seems to me a large digression that is
taking place.
Rather than a resolution it seems to be ballooning outward. This is
the effect of multitype operations though I have not exposed it here.

The issue of a transcenedental number within the real numbers is a
hindsight issue.
It does not serve as a motivation in the definition of ring. If
anything it obscures it.
In terms of the polynomial itself this is merely an issue of
redundancy that has been pointed out. Redundancy is acceptable to me
and I do not feel motivated or enlightened by a system which would
rely upon a transcendental number in order to safeguard from
redundancy. The ground was built from such simple symbollism as
1 + 1 = 2
and so the redundant behavior will never be gotten rid of. It is
within the transcendental number and the prime number.

I'll have to study the polynomial away from the abstract algebra
context to understand how you have wound up where you are at. I have
no problem with the ring definition. But the polynomial usage that is
somewhow productive to you does not yield for me in its abstract form.
I see only the set that it was defined on and nothing more. Upon
defining a set for x then the polynomial does some great things. One
thing it does not do is widen out that set into some new superspace.
Then I can use the ring definition comfortably again.

Well it seems you aren't really interested in pursuing this anymore,
and obviously have some private interpretation of what I've been
trying to explain that leads to difficulties. Unfortunately you seem
neither willing to try and work out why this interpretation must be
wrong and develop a more accurate interpretation, nor to explain what
exactly this interpretation is so I can help you change to a more
correct understanding of what I am trying to communicate. This makes
it rather difficult.

As to transcendentals: the question is essentially this -- how can we
extend the integers by a single element so as generate the largest
possible (and hence most general/universal) ring if we take the
closure of the extended set under ring operations (in this case, ring
operations in the reals).

This is certainly not a ring context you are working in.

Again: given that you do *not* understand what the hell a ring is, how
on Earth do you have the chutzpah to make pronouncements such as the
above?

It is a basis type of concern.

The most basic type of concern should be "how can anyone pretend to
speak authoritatively about a subject which, by his own admission, he
does not understand, is not interested in understanding, does not
know, and is not interested in knowing?" That would seem to me to be a
much more basic concern, but it is clear that such niceties as
"knowing what one is talking about" are simply no bar to your
"genius".

Again, let me disabuse you of your deeply held illusion that you know
what you are doing: you are not. Let me also disabuse you of the
illusion that your verbiage makes you sound interesting, learned, or
deep; in fact, it makes you sound like what you are: a fatuous
ignoramus who has no idea what he is talking about, and hopes the
bluff will hold.

--
Arturo Magidin

Thanks for the unobtuse disabuse.
There is no direct conflict found in my words here Arturo. Your
criticism is strong but it is lacking in mathematical content. If
anything this sort of argumentation is evidence that I have hit
something, rather than that I have it all wrong, for you have not
identified any false statement that I have made.

Son, your messages are FULL of false statements, but only in those
parts where the written stuff isn't plain pompous, fatuous and hollow
stupidity. KMF already showed this in a rather comical fashion.

I'm almost 100% that you must be a rather bored, ignorant ex-beginner
student in mathematics who, being uninterested or, most likely, unable
to study seriously mathematics, just convinced yourself that it'd be
a good idea to come and bug mathematicians with your idiocies...this,
of course, in the best of the cases. In the worst case you REALLY
believe all the nonsense you've written in this thread, what would
automatically turn you into one of the most stupid individuals ever in
visiting this NG.

I wonder how come so many actual mathematicians took so much of their
time trying to drill in some sense into that obviously greymatterless
brain of yours, but I guess that, just like me, they take their
participation in this kind of threads as some light entertainment.

Let us hope that you really don't believe all the nonsenses you've
written here, and let us all hope, in case you really have some
minimal serious interest in learning some mathematics, that you'll
finally grab some damn books and begin reading AND understanding them
(though the greymatterless thing will make this a rather challenging
feat)

In the meantime, I'd advice you to drop dead, but I'm afraid you'll
find something faulty in that, so...do whatever you want.

(dis)Regards
Tonio

Without the pomp and color there will be little discussion. Such is
the closed nature of these topics in the biblical interpretation.
There are enough common instances of mistakes made by scientists as
much as by religionists and the two do become indistinguishable under
attitudes such as yours. I am free to express myself here and I am
grateful to be able to receive back responses here which help to
develop the bifurcation that is visible. Your response is in the realm
of the nonmathematical. I would simply argue to you that when any
supposition in any book is made that it deserves skepticism. When that
supposition has been repeated in enough books and by enough people it
does not make that supposition any more accurate. Further your own
deference to the bright minds that came before you will not serve to
further the mathematics. The development of all topics will come in
challenging what has come before. Rather this is one form of
development. The other which is the more common academic form it that
of tendrilling out to accumulate the structure to a larger extent.
This latter form of accumulation I find difficult and prefer to work
toward the roots of this structure. Best of all the attitude that
there remains something fundamental left to construct keeps the topic
lively rather than stale. These fundamental discoveries will be far
and few between yet I can prove a few that exist. See
http://BandTechnology.com .
I do not believe that you will find the inverse cone construction nor
the polysign construction in the existing literature. Now, polysign
has been expressed in the terms of this mathematics at hand. On one
side of the coin, I can see that my own psyche could sabbotage this
math in order to keep my own construction alive. Yet while I can admit
my own attachment to the idea of polysign numbers, I see that my
presentation is already worlds simpler that the abstract algebra build
of them. I believe that I could teach a sixth grader polysign and that
in learning it their own sign errors on the reals would disappear and
their perception of complex numbers and time will bring to them a
tangibility at an early age beyond what modern mathematics can
provide.

Getting back to the subject at hand though I see no need to drag
polysign into it directly. I wonder how often you would be comfortable
invoking the freedoms that the polynomial in X brings into an existing
math? On any set one might declare such freedoms. I do sincerely
believe that this ultraset brought about through the polynomial
interpretation is questionable. Could I for instance invoke
A[Y[X]] ?
Is this then a set larger than A[X]? I have not gone to the trouble
here of attempting this but I suppose for someone more advanced than
myself this level ought to be considered. Under my simplistic
interpretation upon specifying A this will collapse to A but through
the universalist approach this new construction is that much more
universal than the one which came before it:
Z is in R is in C is in ... A[X] is in ... A[Y[X]] ...
Maybe that should be A[X[Y]]- I'm not really sure. Regardless I need
not believe in this construction to carry on with the subject matter.
The scholarly religionist might study the Torah and the Bible yet obey
the Koran. It is their free right to likewise construct their own book
since these previous books are merely constructions. Thus comes forth
the Bahai religion and so forth:
http://en.wikipedia.org/wiki/Bahai

- Tim



- Tim
.

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