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Recent Comments
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
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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
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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
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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
33 Comments
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
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