 In this context, an incomplete path in spacetime is one that is both inextendible and of finite proper length, which means that any particle or observer traversing the path would experience only a finite interval of existence that in principle cannot be continued any longer. For this criterion to do the work we want it to, however, we will need to limit the class of spacetimes under discussion. Specifically, we shall be concerned with spacetimes that are maximally extended (or just ‘maximal’, for short). In effect, this condition says that one's representation of spacetime is “as big as it possibly can be”. There is, from the mathematical point of view, no way to treat the spacetime as being a proper subset of a larger, more extensive spacetime. (See  figure 2.)  