In these days in which "exponential growth" has such ominous connotations, we are pleased to announce our new paper which includes fast-growing functions in a much lighter setting. Fusible numbers and Peano Arithmetic. https://arxiv.org/abs/2003.14342 . Joint work with @jeffgerickson and @alreadydone

Consider the algorithm "M(x): if x<0 return -x, else return M(x-M(x-1))/2". This algorithm terminates for all real x, though this is not so easy to prove. In fact, Peano Arithmetic cannot prove the statement "M(x) terminates for all natural x". Paper to come! Joint work with @jeffgerickson and @alreadydone