Recent content by Oster

  1. O

    Prove that the extension is Normal

    Prove that the field Q(√2,√3,u) where u^2=(9-5√3)(2√2) is normal over Q. I'm supposed to show that this field is the splitting field of some polynomial over Q. u is clearly algebraic over Q. Do i just take the higher powers of u and try to find the minimal polynomial over Q or is there a...
  2. O

    Cancellation of Groups in Internal Direct Products

    H and K need not be finite. And I don't see why your second claim should hold. Can you explain a bit more please?
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    Cancellation of Groups in Internal Direct Products

    G, H, K are groups. G is finite. GxH is isomorphic to GxK. Prove H is isomorphic to K. Give an example to show that this does not hold when G is infinite. The counter example when G is infinite is Rx{0} and RxR (R - real numbers) I'm having trouble Proving the main part of the question. I...
  4. O

    Question about Normed Linear Spaces

    Thank you!
  5. O

    Question about Normed Linear Spaces

    Statement: V is a finite dimensional vector space with basis {ei} (i goes from 1 to n). V has a norm || || defined on it(not necessarily induced by an inner product). Let x=Ʃxiei belong to V. I want to show that ||x|| ≥ ||xiei|| for any fixed i. I'm not entirely sure this result is correct...
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    Prove its abelian is this proof correct

    Your proof is a little hard to read. In your proof you seem to have proved ab=e for all a,b in G? that looks fishy... this is a solution. https://www.physicsforums.com/showthread.php?t=529381
  7. O

    Functions - is this proof satisfactory?

    Its not so clear to me. If f(x) = f(y) for some x,y in A you have to show x=y.
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    Function bounded on [a,b] with finite discontinuities is Riemann integrable

    Thats the idea. You can choose c_j''-c_j' to be less than some multiple of epsilon and then proceed.
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    Function bounded on [a,b] with finite discontinuities is Riemann integrable

    You're almost there! You can choose your c_j'' and c_j' to be as close as you want, can't you?
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    Nilpotent Matrices: Invertibility and Transpose Proof

    A matrix is invertible if and only if it has non-zero determinant. What can you say about the determinant of a nilpotent matrix? C. You could prove this by assuming it is false i.e. I-A is not invertible and then proceeding.
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    Equivalence of Subgroups in a Group

    Reflexive means a~a. Can you find an element in H and another in K such that a=h.a.k? Symmetric means a~b => b~a. So if a=h.b.k, you need to show b=h'.a.k' for some h' in H and k' in K. Just use the definitions...
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    Completeness of R^2 with sup norm

    I thought x_n was your arbitrary Cauchy sequence. You have an x_n and an x in your post.
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    Completeness of R^2 with sup norm

    Where did your x come from? Cauchy means for all r>0, there exists a natural number p such that for all m,n>p, d(x_m,x_n) < r. In this case, max{|xn(1)-xm(1)|,|xn(2)-xm(2)|}<r for all n,m>p
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    Improper Integral question: Convergence of 1/(x^p) from 0 to 1

    Hmm, I have no idea what 'in terms of area' means. Sorry. Ignore? =D
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    Improper Integral question: Convergence of 1/(x^p) from 0 to 1

    I think they want you to integrate with respect to y instead of x.