Re: Understanding the quotient ring nomenclature

Tim BandTech.com wrote:
On Jun 16, 5:22 am, Brian Chandler <imaginator...@xxxxxxxxxxxxx>
wrote:
<snip>
"Criticism" isn't the problem. But you still _haven't_ explained. Do
you understand why saying "the (set of) polynomials form a ring" is
true, and the bits about "polynomials are not rings" is not false, but
just meaningless.
, or are you telling your own story
You still don't appear to intend to tell us. Never mind...

The definition of ring provides superposition and product operators.

It does? Here's a definition of a ring, randomly plucked from
Wikipedia:

In mathematics, more specifically in modern algebra, a ring is a set
equipped with two binary operations – often referred to as addition
and multiplication.

Are you using "superposition" to refer to the addition operation? Or
something else? Are you attempting to talk about what mathematicians
mean by rings?

These are the same operators in use within the polynomial. Because
superposition requires that each of its elements be in the same domain
then any work in polynomials with real coefficients must obey the
superposition operator.

Seems not. Pity. You may be a misunderstood genius, for all I know,
but you will remain thus unless you are prepared to understand what
other people are saying, so you can talk to them in a way that leads
to understanding, not just more confusion.

Brian Chandler
.

Relevant Pages

  • Re: Understanding the quotient ring nomenclature
    ... "Criticism" isn't the problem. ... The definition of ring provides superposition and ... what is the superposition operator? ... the discussion of polynomials (over ...
    (sci.math)
  • Re: Understanding the quotient ring nomenclature
    ... say "the polynomials are not rings" which is fundamentally wrong. ... The definition of ring provides superposition and product operators. ... conflicts are that which mathematics is not. ...
    (sci.math)
  • Re: Possible flaw in the polynomial ring A[X] construction
    ... distinguish it from the product of polynomial functions. ... for rings of finite characteristic, so let us consider the base ring to ... the ring of polynomials over this field is ... with the base ring being the field of two elements. ...
    (sci.math)
  • Re: Possible flaw in the polynomial ring A[X] construction
    ... with further operations such as a quotient ring. ... then the ring Aof polynomials with real coefficients, ... than just heaping piles of construction upon other piles of ... "While the polynomial itself is necessarily infinite in length, ...
    (sci.math)
  • Re: Understanding the quotient ring nomenclature
    ... A ring is defined as containing elements. ... undefined domain and an infinite length of terms. ... infinite series are reals. ... long as the two polynomials being multiplied have finitely many terms, ...
    (sci.math)