 Overall, the three volumes not only represent a major leap forward with regard to modern logic, they are also rich in early twentieth-century mathematical developments. To give one example, Whitehead and Russell were the first to define a series as a set of terms having the properties of being asymmetrical, transitive and connected (1912 [1927: 497]). To give another, it is in Principia that we find the first detailed development of a generalized version of Cantor’s transfinite ordinals, which the authors call “relation-numbers”. The resulting “relation-arithmetic” in turn led to significant improvements in our understanding of the general notion of structure (1912: Part IV).