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Homework Help: Helpe me

  1. Jun 2, 2008 #1
    1. The problem statement, all variables and given/known data

    three quistions':
    1) What is a meaning of (homotopic) in Cauchy's theorem for the sets'?
    and in sets what is t,s where H(t,s)

    2)
    (-1)^1/2*(-1)^1/2 = (-1*-1)^1/2=1^1/2=1=/=i^2




    3)
    In Integral functions' by Reiman Sum
    is delta x
    It handles any inclination at the point
    Concluded that by diminishing its value to zero

    2. Relevant equations



    3. The attempt at a solution

    2) (-1)^1/2*(-1)^1/2 = i(1)^1/2*i(1)^1/2=i*i=-1=/=1
    But the former right way
    The result is wrong
    logic Sports saysThe right does not lead to an error
     
  2. jcsd
  3. Jun 2, 2008 #2

    HallsofIvy

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    Science Advisor

    Two paths in a topological space (or the functions defining those paths) are said to be "homotopic" if one can be "continuously deformed" into the other. More specifically, if f:R-> X is a function from the real numbers to a space X (so that f defines a one-dimensional path in X) and g:R->X is another, then f and g are homotopic if and only if there exist a function [itex]\Phi(t, u)[/itex] where [itex]0\le t\le 1[/itex], u is real number, continuous in both t and u, and such that [itex]\Phi(0, u)= f(u)[/itex], [itex]\Phi(1, u)= g(u)[/itex].

    I don't recognize this. What is H? What area of "sets" do you mean? Since you mention "homotopic" could this be a homotopy group?


    No, axbx= (ab)x does not, in general, hold for complex numbers.



    "Inclination"? I think that's a mis-translation. delta x measures the slight change in x on which you are basing your Riemann Sum.

    It's a bit more complicated than that. You must let delta x go to 0 while, at the same time letting the number of terms in the sum go to infinity. In any case, I see no question here.

    "logic" doesn't work if you start from incorrect premises. As I said above, axbx is not generally true for complex numbers. It is the "former" that is wrong. The definition of "1/2 power" or square root, is that (a1/2)(a1/2)= (a1/2)2= a for any complex number a. (-1)1/2(-1)1/2= -1 is correct.
     
    Last edited by a moderator: Jun 2, 2008
  4. Jun 2, 2008 #3
    Thanks you the abundant thanks
    :rolleyes:
     
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