If we treat light as a wave. Sin(nx)
do we say white light consists of many functions where n can be an element of Real positive numbers?
or are they intergers?
White light at a point is a combination of many terms of the form $\displaystyle \sin(2 \pi f t +\phi)$, but the frequencies can be any real number (that is we have a continuous spectrum).
A casual observer cannot tell the difference between a continuous and discrete spectrum because of the way that the eye works, so what you think is white light need not have a continuous spectrum
RonL