A continuum has all of the infinity of possible values "in-between" any pair of values, no matter how small the difference between those two values.  Our mathematics usually assumes that all of those values are in fact possible.  Quantum mechanics was the discovery that this is wrong.  The wavelength of a photon (the indivisible "unit" of light) is determined by structures within atoms and molecules, and more specifically, the "energy levels" associated with those structures.  Not all levels are possible, and so not all wavelengths are possible.  The elementary math we learned in elementary school, and use for real-world problems, is always an approximation. 

Statistical mechanics and wave mechanics comprise the truly appropriate math.  The functions are discontinuous, not smooth.  The numbers are probabilities, not certainties.  Influences are multiple and subtle, not single and simple.  We are fortunate that our grade school math does often give us good approximations.

But there is, lurking beneath the obvious, a much richer reality.