sentences:  Consequently, we rely on the stronger definition above which implies that the irrationals are typical and the rationals are not.For applications, if a property holds on a residual set, it may not hold for every point, but perturbing it slightly will generally land one inside the residual set (by nowhere density of the components of the meagre set), and these are thus the most important case to address in theorems and algorithms.A property is generic in "Cr" if the set holding this property contains a residual subset in the "Cr" topology.