Arturo Magidin a écrit : > On Jun 6, 9:44 am, "Tim BandTech.com" <tttppp...@yahoo.com> wrote: > >> Thanks. It certainly does feel vague. For instance if I were to build >> a polynomial in this X with real coefficients such as >> - 5.2 XXX + 2.3 XX - 1.1 X - 0.23 >> I'd have rather a lot of trouble evaluating this for a given X if X is >> undefined. > > You are confusing polynomial *functions* with polynomials. Polynomials > are not "evaluated". You don't need to "evaluate for a given X". (And, > on the other hand, if you have a polynomial *function*, then a "given > X" would, *of course*, not be "undefined": it would be *given*). > >> On the other hand, if X is real > > X is not a real. These things are not *functions*, they are > *polynomials*. > >> then regardless of what I >> put in this expression the result is likewise real. > > These are not expressions to be evaluated, they are polynomials. > >> Somehow >> mathematicians are comfortable working with objects which are not >> clearly instantiated. > > Polynomials *are* "clearly instantiated". The problem here is not > about what mathematicians are or are not comfortable working with, but > rather that you are confusing two things (not your fault: in high > school most people are not told of the distinction). Polynomials and > polynomial functions are *different things*. See Bill Dubuque's post > if you want a particular way of instantiating polynomials as almost > null sequences. > > >> I'm afraid that at this level of discussion I'm >> dealing in several of these stacked uninstantiated objects. > > I'm afraid that the real problem is that you are a bit confused about > the objects in question, and that there are some rather large lacunae > in your knowledge of the things you need to understand these objects. > Again, not your fault, but you are trying to run a marathon without > knowing how to move your feet. > > >> Above here Arturo states: >> >> "R is the ring of real numbers, X is an indeterminate variable, and >> R[X] is the ring of polynomials with coefficients in R." >> >> yet this does not wash since there are three devices described in a >> notation of just two devices. > > If by "this does not wash" you mean "I do not understand", then you > are correct. The problem here is that you are not understading, not > that anyone is hiding anything from you. > > The ring of polynomials S[T], with S a ring and T a set is > *completely* determined by specifying S and T. The "third object" is > *constructed* from the first two. > > >> The polynomial has a clear description >> as a sum >> sum over n ( a(n) X ^ n ) >> yet is never actually invoked within the description. > > And now you are confusing a *particular* polynomial with the ring of > *all* polynomials. R[X] is the ring of *all* polynomials with real > coefficients, not a particular one. See? It's not that what I said > "does not wash": it's that you are not familiar enough with these > things to understand what is being said. > >> The meaning of X has been scuttled. > > Nonsense. > >> Your interpretation seems more believable but you >> say it is not the truth. > > Look: nobody is lying to you. The problem here is that you are simply > not aware of the context and the background necessary to understand > the answers you are given, but you are now blaming those answering you > and even accusing them of lying to you, because you don't understand > the answers. > > Nobody is lying to you. Nobody is hiding the truth. What you need to > do is learn a bit more about rings and polynomial rings in order to > understand the answers you are being given. > >> I guess that one simple question to get answered is: >> Is X real valued? > > Sigh. You are not dealing with a specific polynomial nor with > polynomial functions. Your question may be simple, but it is in fact > quite meaningless in this context. Just as if you were asking "what > color are ideas that dream furiously?". >
I know that one, I do. Can I answer, teacher? Can I ? > -- > Arturo Magidin
