The concept of $q$-deformation, or ``$q$-analogue'' arises in many areas of mathematics. In algebra and representation theory, it is the origin of quantum groups; $q$-deformations are important for knot invariants, combinatorial enumeration, discrete geometry, analysis, and many other parts of mathematics. In mathematical physics, $q$-deformations are often understood as ``quantizations''. The recently introduced notion of a $q$-deformed real number is based on the geometric idea of invarianc...
