You can play the individual notes of a chord on one piano or several, but they still come together to produce the same chorus of frequencies.
The Fourier series representation of a waveform is itself a sum, since trigonometric functions are waveforms as well. Thus, a combination thereof should be commutative because a sum of two sums retains the properties of addition.
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Here's how I think about it.
You can play the individual notes of a chord on one piano or several, but they still come together to produce the same chorus of frequencies.
The Fourier series representation of a waveform is itself a sum, since trigonometric functions are waveforms as well. Thus, a combination thereof should be commutative because a sum of two sums retains the properties of addition.