
Recent Posts
Subscribe to Complex Projective 4Space
Archives
 September 2021
 July 2021
 June 2021
 May 2021
 February 2021
 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
 Ross Presser on Hamming backups: a 2of3 variant of SeedXOR
 An efficient prime for numbertheoretic transforms  Complex Projective 4Space on Complexity of integer multiplication almost solved
 SuperSupermario24 on Infinite monkey theorem
 Daniel Sebald on Gosper’s Pyrominia animation
 Daniel Sebald on Rational approximations to Platonic solids
Monthly Archives: December 2013
New Year’s Eve
It’s now New Year’s Eve, which is why the cp4space banner has changed again. As is usual for this time of year, there is a joint AngloHungarian IMO training camp in Tata, Hungary. I’ve mentioned it before at the end of 2012, … Continue reading
Posted in Uncategorized
4 Comments
Applications of ultrafilters
This is the sequel to the previous article defining ultrafilters and establishing basic properties thereof. Again, the proof of Hindman’s theorem is from Imre Leader’s lecture course on Ramsey theory. It seems initially paradoxical that ultrafilters are actually useful. After … Continue reading
Posted in Uncategorized
Leave a comment
Comprehending ultrafilters
This is the first of a projected twopart series of articles about ultrafilters. The former introduces ultrafilters and establishes various properties about them, so that the latter article can concentrate entirely on applications of ultrafilters. Much of this material is from Professor Imre … Continue reading
Posted in Uncategorized
4 Comments
Large cardinals
(This article is about the axioms concerned with the existence of enormous sets. If you were instead looking for corpulent subordinates of the Pope, then I suggest watching this Monty Python sketch.) How big is the universe? Ultrafinitists such as Doron … Continue reading
Posted in Uncategorized
16 Comments
Tarski’s circlesquaring problem
Is it possible to dissect a square into finitely many pieces, which can then be rearranged to form a disc of equal area? Note that, unlike in three dimensions where the BanachTarski paradox exists, dissections must respect the twodimensional Banach measure … Continue reading
Posted in Uncategorized
Leave a comment
Free commutative monoid on countably many generators
Consider the following problem: Let be a finite set of positive integers. Suppose we colour the positive integers with k distinct colours. Prove that there exist constants a and b such that is monochromatic. Initially, this seems as though it … Continue reading
Posted in Uncategorized
3 Comments
Miscellaneous news and sphere eversion
Before we begin, there are a few late items of news worth discussing: There is a free edition of Wolfram Mathematica for the Raspberry Pi, an increasingly popular versatile lowcost computer. More details are available over at The Aperiodical. The … Continue reading
Posted in Uncategorized
Leave a comment