Category Archives: Fast-growing functions

There have been many exciting results proved by members of the Googology wiki, a website concerned with fast-growing functions. Some of the highlights include: Wythagoras’s construction of an 18-state Turing machine which takes more than Graham’s number of steps to … Continue reading →

This is the final article on fast-growing functions. In the first two articles we looked at computable functions, up to and including Friedman’s TREE function. The third article described the Busy Beaver function, which eventually overtakes all computable functions. This … Continue reading →

This is the third out of a series of four articles on increasingly fast-growing functions. The first article described the Ackermann function (corresponding to ω) and the Goodstein function (corresponding to ε_0). The second article went into much more detail about a … Continue reading →

This is the first of a projected two-part series of articles about fast-growing functions. The first part (‘fast-growing functions’) will introduce the concept of a fast-growing hierarchy of functions, use some notation for representing large numbers, make an IMO shortlist problem infinitely more … Continue reading →