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B Is a (binary) number a basis?

  1. Jun 30, 2016 #1
    Could you view a discrete number, for instance a binary number, as a sort of orthogonal basis, where each digit position represents a new dimension? I see similarities between a binary number and for instance Fourier Transform, with each digit being a discrete function.
     
  2. jcsd
  3. Jun 30, 2016 #2

    Grinkle

    User Avatar
    Gold Member

    How is that different from writing out a vector?

    [1 0 1 1 1 0]

    vs

    101110

    Isn't it just a matter of notation and interpretation? The algebra for manipulation doesn't change, I think? There may be a deeper question than I am seeing, I am far from a mathematician.
     
  4. Jun 30, 2016 #3

    fresh_42

    Staff: Mentor

    Yes. Since ##\mathbb{Z}_2## is a field everything is fine in ##\mathbb{Z}_2^n##, the ##n-##dimensional unit cube.
    You might want to have a look on the following page https://en.wikipedia.org/wiki/Discrete_Fourier_transform about discrete Fourier transformations which are an important tool in information theory.
     
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