  Now clearly, in modern language, one should say in the second case that the trajectory lies densely in the surface, but not that it traverses all points. Boltzmann did not possess this language. In fact, he could not have been aware of Cantor's insight that the continuum contains more than a countable infinity of points. Thus, the correct statement that, in the case that \(\sqrt{a/b}\) is irrational, the trajectory will traverse, for each value of \(x\), an infinity of values of \(y\) within any interval however small, could easily have lead him to believe (incorrectly) that all values of \(x\) and \(y\) are traversed in the course of time.