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    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...
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    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...
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    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...
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    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.
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    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...
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    Proving the uniqueness of a polynomial

    If a polynomial p(x)=a_0+a_1x+a_2x^2+ \ldots +a_{n-1}x^{n-1} is zero for more than n-1 x-values, then a_0=a_1= \ldots =0. Use this result to prove that there is at most one polynomial of degree n-1 or less whose graph passes through n points in the plane with distinct x-coordinates. Let p(x) be...
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    Linear Algebra linear transformation question

    Let the set S be a set of linearly independent vectors in V, and let T be a linear transformation from V into V. Prove that the set {T(v_1), T(v_2),...,T(v_n)} is linearly independent. We know that any linear combination of the vectors in S, set equal to zero, has only the trivial solution...
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    Orthogonal complement question

    I have the set s = span ( [[0][1][-1][1]]^{T} ) And I need to find the orthogonal complement of the set. It seems like it should be straight foward, but I'm a bit confused. I know that S is a subspace of R^4, and that there should be three free vairables. What I did so far is to take the...
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    Finding a basis for a subspace of P_2

    Let W=\lbrace p(x) \in P_{2} : p(2)=0\rbrace Find a basis for W. Since a basis must be elements of the set W we know that p(2)=0. So if p(x)=ax^2+bx+c, then p(x) = 4a+2b+c=0. Let c=t, b=s and s,t are real scalars. Then p(x) can be written as t(-\frac{1}{4} x^2+1)+s(-\frac{1}{2}x^2+x)...
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    Easy electric charge question

    Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters. The electrostatic force acting on sphere 2 due to sphere 1 is F and the force acting on sphere 1 due to sphere 2 is -F'. Suppose now that a third...
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    Deductive Essay

    I would appericate it if someone here could look over my essay and post some comments. The things to look for are: Varied wording Grammer and spelling Good sentence structure Good paragraphs Verb tense Anything else that you find wrong with the paper. It's suppose to be...