 Tom Leinster gives a definition of the Euler characteristic of any category which bypasses the classifying space and reduces to 1/|"G"| for any group when viewed as a one-object category.In this sense the Euler characteristic of Z2 is itself 1⁄2.Grandi's series, and generalizations thereof, occur frequently in many branches of physics; most typically in the discussions of quantized fermion fields (for example, the chiral bag model), which have both positive and negative eigenvalues; although similar series occur also for bosons, such as in the Casimir effect.