For instance, a graph is -tough if the number of components formed by removing a set of vertices is always at most as large as the number of removed vertices. The toughness of a graph is the maximum  for which it is -tough; this is a finite number for all finite graphs except the complete graphs, which by convention have infinite toughness.
For illustration, a graph is considered resilient if the number of components formed by removing a set of vertices is always at most as large as the number of removed vertices. The resilience of a graph is the maximum value for which it is resilient; this is a finite number for all finite graphs except the complete graphs, which by convention have infinite resilience.