To trace the ergodic condition, I have turned to trajectories in the logistic map. According to the theorem of Sharkovskii, chaos exists where 3-cycle exists. To show chaos, one has to first solve for the fixed points of 3-cycle, which turns out to be a sextic equation. The analytical solutions allow one to realize chaos and chaotic trajectories via an aleph cycle. An aleph cycle spans a field of all irrational points in an interval but not of rational points. One can thus see that the ergodic condition refers to a set of points of measure zero on ergodic surfaces. When time averages are actually calculated for dynamical variables of macroscopic systems, this set of points of measure zero does not contribute. This is why this particular ergodic condition does not appear in the ergometric theory.