Up to the present time [1965], only magnetic configurations that are continuous in the micromagnetic sense have been described in the literature. The consequences of this continuity restriction on possible types of magnetization reversal processes have received no attention. These consequences are discussed here. It is also shown that micromagnetic discontinuities are allowed theoretically. In particular, a micromagnetically singular point may exist that is the zero-dimensional analog of the two-dimensional wall and the one-dimensional Bloch or Neel line of magnetic domain theory.