[synergy7]

Weierstrass function is used prominently in Abbot's (2015) "Understanding Analysis" book. Abbott also relies heavily on three other mind-bending functions - Dirichlet (nowhere continuous), Thomae (discontinuous at every rational and continuous at every irrational point), and Cantor (increasing and continuous on [0, 1], yet constant at [0, 1]\C. where C is the Cantor set that is of measure zero).

Dirichlet, Thomae, and Cantor functions are central in Abbott to introduction and exercises on continuity, differentiation, and integration. I thought that was an interesting pedagogical choice for an undergraduate book, especially when it is used for the very first course in mathematical analysis as in Princeton’s MATH215 (I do think it is a really nice book).