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Commutator of f(x) and x

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Is the commutator of x and any function of x zero?


    2. Relevant equations
    Taylor's theorem allows such a function to be expanded into polynomials, so that [f(x),x] may be expanded into terms of [x^n,x], which are all zero. Hence, f(x) and x commute.

    3. The attempt at a solution

    Is this a valid demonstration?
     
  2. jcsd
  3. Sep 18, 2011 #2

    kuruman

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    You don't need a Taylor expansion. What do you think is x(f(x) - f(x)x?
     
  4. Sep 19, 2011 #3

    dextercioby

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    This is true iff X and f(X) have the same domain, i.e. the domain of X is invariant.
     
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