Magnitude of discontinuity In the discussion of Fourier series it is said that the Fourier series representation of a discontinuous function will overshoot its value at a discontinuity. Although as more terms are included the overshoot moves in position arbitrarily close to the discontinuity, it never disappears even in the limit of an infinite number of terms. This behavior is known as Gibbs’ phenomenon. In layman's terms, the size of the overshoot is proportional to the magnitude of the discontinuity. Now what is meant by the "magnitude of discontinuity"?

If $\lim_{x\to a^-} f(x) = L^-$ and $\lim_{x \to a^+} f(x) = L^+$, then the magnitude of the discontinuity is, by definition, $|L^+-L^-|$.