  The innovation that gives intuitionism a much wider range than other varieties of constructive mathematics (including the one in Brouwer’s dissertation) are the choice sequences. These are potentially infinite sequences of numbers (or other mathematical objects) chosen one after the other by the subject. Choice sequences made their first appearance as intuitionistically acceptable objects in a book review in 1914; the principle that makes them mathematically tractable, the continuity principle, was formulated in Brouwer’s lectures notes of 1916. The main use of choice sequences is the reconstruction of analysis; points on the continuum (real numbers) are identified with choice sequences satisfying certain conditions. Choice sequences are collected together using a device called  “spread”, which performs a function similar to that of the Cantorian set in classical analysis, and initially, Brouwer even uses the word “Menge” (“set”) for it. Brouwer develops a theory of spreads, and a theory of point sets based on it, in the two-part paper “Founding Set Theory Independently of the Principle of the Excluded Middle” (1918/1919).