I know that signals that are orthogonal do not disturb each other.
What I am curious is what is the proof behind why orthogonal signals in a single signal (i.e. a single signal can be broken down into signals that have their unique frequency.) do not disturb each other so that Fourier transform can be carried out.
Edit: By signals not disturbing each other, I mean that when Fourier transform into frequency contents is carried out, each signal's frequency content is not disturbed. For example, harmonic signals (waves). two signals, each with frequency $f$ and $2f$ are combined into one signal. When the signal is received, a receiver can figure out the two signals that were combined. Similar with OFDM. According to the text, it says that this is due to its orthogonal nature. I get what orthogonality mean, but I am not sure how being orthogonal leads to non-disturbance of signal components.