Is a (binary) number a basis?

  • #1
entropy1
Gold Member
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53

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
Grinkle
Gold Member
660
184
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.
 
  • #3
12,691
9,235
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.
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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