You know that a sine corresponds to a pulse by J.Fourier transform. The lower is the frequency, the closer is the pulse to the origin. A constant signal is a sine (or cosine, that may be important) of frequency 0. It is a pulse in the origin. This is ok, since we know very well that a pulse transforms to the white spectrum: it is a combination of all sine waves at once.
But, I see a contradiction here. I have just shown that a constant is also a sine of frequency 0 and, also, a combination of all frequencies. A sine of frequency 0 is a sum of all frequencies. How is this possible?