
Recent Posts
Subscribe to Complex Projective 4Space
Archives
 January 2021
 December 2020
 November 2020
 October 2020
 September 2020
 August 2020
 July 2020
 June 2020
 May 2020
 June 2019
 May 2019
 March 2019
 November 2018
 September 2018
 July 2018
 June 2018
 May 2018
 April 2018
 March 2018
 February 2018
 November 2017
 October 2017
 November 2016
 May 2016
 March 2016
 February 2016
 December 2015
 September 2015
 March 2015
 February 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
Recent Comments
 Meagre sets and null sets  Complex Projective 4Space on Fat Cantor set
 apgoucher on The neural network of the Stockfish chess engine
 Jeremy Bearimy on The neural network of the Stockfish chess engine
 Johnnycanspell on The neural network of the Stockfish chess engine
 apgoucher on The neural network of the Stockfish chess engine
Category Archives: Fastgrowing functions
Fastgrowing functions revisited
There have been many exciting results proved by members of the Googology wiki, a website concerned with fastgrowing functions. Some of the highlights include: Wythagoras’s construction of an 18state Turing machine which takes more than Graham’s number of steps to … Continue reading
Posted in Fastgrowing functions
7 Comments
Graph minors
This is now, at the time of writing, the longest article on cp4space. We’ll begin with a very wellknown problem, which asks whether it’s possible for three houses on the plane to be connected to three utility suppliers without crossings. What appear … Continue reading
Posted in Fastgrowing functions, Uncategorized
Leave a comment
The Ξ function
This is the final article on fastgrowing 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
Posted in Fastgrowing functions
Leave a comment
Busy beavers
This is the third out of a series of four articles on increasingly fastgrowing 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
Posted in Fastgrowing functions
Leave a comment
TREE(3) and impartial games
This article was originally supposed to be about TREE(3) and the busy beaver function. However, I realised the potential of turning TREE(3) into a twoplayer finite game, which is surprisingly fun and means that I’ve ended up leaving uncomputable functions until a later post. … Continue reading
Posted in Activities, Fastgrowing functions
Leave a comment
Fastgrowing functions
This is the first of a projected twopart series of articles about fastgrowing functions. The first part (‘fastgrowing functions’) will introduce the concept of a fastgrowing hierarchy of functions, use some notation for representing large numbers, make an IMO shortlist problem infinitely more … Continue reading
Posted in Fastgrowing functions
Leave a comment