Recent content by Geekster

  1. G

    Property of a ring homomorphism

    I think I have an answer, let me know if you think my proof is ok. Suppose there exists some a in the reals such that f(a)!=0. Then f(1*a)=f(1)*f(a)=f(a). So f(1) must be the identity in Q. But that allows us to get numbers like 2 since f(1+1)=f(1)+f(1)=2. But then we have...
  2. G

    Property of a ring homomorphism

    Homework Statement Suppose that f:R->Q (reals to rationals) is a ring homomorphism. Prove that f(x)=0 for every x in the reals. Homework Equations Homomorphisms map the zero element to the zero element. f(0) = 0 Homomorphisms preserve additive inverses. f(-a)=-f(a) and finally...
  3. G

    Sequences ratio test, intro to real analysis

    Homework Statement Let X = (xn) be a sequence of positive real numbers such that lim(xn+1 / xn) = L > 1. Show that X is not a bounded sqeuence and hence is not convergent. Homework Equations Definition of convergence states that for every epsilon > 0 there exist some natural...
  4. G

    News Vote Republican

    In reference to the bold text. I don't disagree with your perspective...however, you do know that if a need for a road or service comes up that more often than not people in a local community will get together and form a cooperative effort to help pay for the required service. If you don't...
  5. G

    News Vote Republican

    I guess you missed the part where he talks about the federal government NOT doing things. That is the ONLY thing he wants to do..... To do that he has stated he will get rid of things like the department of commerce, the FBI, the CIA, get the US out of the UN, get the US out of pro corporate...
  6. G

    Trigonometric nastiness

    Well, I, couldn't work it out. But I found that maple can work out the indefinite integral, and the definite integral which as you know is Pi/2. While I don't know how to derive the indefinite integral, with your limits with the following does work out quite nicely. -i \left( \ln \left( x...
  7. G

    Some set proofs

    Disclaimer: I might have some problems getting my LaTeX code to work properly so please bear with me while I figure out how to properly use the forum software. Homework Statement The exercise is to prove the following statements. Suppose that f:X \rightarrow Y, the following statement is...
  8. G

    News Those crazy dems

    link Seems they owe the Bush & Co. a little something..... The overly politicized subject of "Plamegate" now has the truth. The funny thing is that I don't hear any republicans taking this oppertunity to bash the Dems (save for a very few like me) odd.
  9. G

    Vector components under a translation

    I still don't get it....:frown: So let's say I have a vector (1,1,1) using standard basis. Now I want to translate the coordinates so my new origin is at (1,1,1) with the basis vectors being parallel to the standard basis vectors. Then is my vector's coordinates still (1,1,1) relative to the...
  10. G

    Vector components under a translation

    Ok.... I am asked how a vector's components transform under a translation of coordinates. From mathworld: Does that imply that the components used to describe the vector remain unchanged? If you and I see a car drive east at 50 Km/h and you are standing at what you call the origin, and I...
  11. G

    How does a norm differ from an absolute value?

    What the norm is kind of depends on how you are defining the inner product. The example you have is for a normal dot product, but the norm for an inner product is the sqrt of the inner product.... A better definition
  12. G

    Proving the uniqueness of a polynomial

    I see the problem..... You are correct (imagine that, I'm wrong) that a_jx_1^j-y_i=0 is not true for all i and j....only for j=0. I guess I'm gonna have to go back to the method you suggest. I'm gonna work on that....I'll post what I come up with. Thanks
  13. G

    Proving the uniqueness of a polynomial

    Why not? It's stated in the problem that if you have p(x) of degree n-1 with n roots, then all coefficents are 0. So if you have p(x_i)=y_i then consider p(x_i)-y_i=0. Here there are n polynomials all of degree n-1 or less, and together there are n roots. Therefore the coeffiencts of p are all...
  14. G

    Integral and cylindrical shell

    I think I see where you are getting confused...there is a difference between what x varies over, and what the bounds are. In this case x varies from 0 to 2. That is different from a bound. Suppose the curve y=x^2 was bounded by y=0, and x=1, but x varied from 0 to a billion? It doesn't much...
  15. G

    Proving the uniqueness of a polynomial

    Let me better define my function. Let p:R->R be defind such that p(x_i)=y_i and p(x) is a polynomial, and the coefficents of p(x) are not necessarily distinct. True, but we are just talking about p(x) (now better defined) and we know that the a_jx_i^j-y_i=0 where j=0,1,...,n-1 and...