I am writing my thesis on quasi-periodic oscillations, which are signals containing two frequencies (let's leave it by that for now) with an incommensurable (irrational) ratio. However, I am a trained engineer and need a mathematical sharpening of my language:
The problem of quasi-periodic oscillations is that the frequencies constitute a Cantor set, since rationally dependent frequencies lead to periodic oscillations.
I know that the irrational ratios or - in general - irrational numbers constitute a Cantor set of positive measure within the real numbers. I just do not understand why it has positive measure. What about the density of the set?
Thank you very much!