Re: Understanding the quotient ring nomenclature

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
.

Relevant Pages

  • Re: Understanding the quotient ring nomenclature
    ... It does not serve as a motivation in the definition of ring. ... redundancy that has been pointed out. ... Then I can use the ring definition comfortably again. ... neither willing to try and work out why this interpretation must be ...
    (sci.math)
  • Re: Understanding the quotient ring nomenclature
    ... It does not serve as a motivation in the definition of ring. ... redundancy that has been pointed out. ... neither willing to try and work out why this interpretation must be ... student in mathematics who, being uninterested or, most likely, unable ...
    (sci.math)
  • Re: Possible flaw in the polynomial ring A[X] construction
    ... different ring*. ... all the polynomials would get ... just other humans looking over your ... My arguments on this thread do rely upon the ring definition, ...
    (sci.math)
  • Re: Possible flaw in the polynomial ring A[X] construction
    ... provided by the ring definition. ... larger than the base ring (the reals in your case). ... the ring of polynomials as a set is really like the cartesian ...
    (sci.math)
  • Re: Possible flaw in the polynomial ring A[X] construction
    ... which I am holding on to is that when A is real valued that A ... The ring provides operators sum and product. ... there is no multidimensional interpretation present. ... just as I find fault with the existing construction by that ...
    (sci.math)
Quantcast