4 ms·
The road to epsilon-zero: Nim always ends, even with infinite ordinals
- linzhangrun 3mo agoFirst glance I thought someone was referring to https://nim-lang.org/ https://nim-lang.org/
- HeavyStorm 3mo agoMe too. Why I clicked the link.
- xelxebar 3mo agoUsing ordinals to talk about finite numbers gets suprisingly deep real fast. David Metzler has a series of fun videos called "Ridiculously huge numbers" that goes down the rabbit hole of the fast growing hierarchy. https://www.youtube.com/playlist?list=PL3A50BB9C34AB36B3 https://www.youtube.com/playlist?list=PL3A50BB9C34AB36B3 BB(n), Rayo's number and friends can get bigger way faster, but they do this uncomputably fast. Launching yourself into arithmetic hyperspace in a controlled way like with the fast growing hierarchy does a much better job of conveying the sheer vastness of finitude. OP's article got me thinking about Nim with added mechanics that let you get all the way to Feferman–Schütte, hence the above.
- mjd 3mo agoOne of my life goals is to fully understand Jean Gallier's paper about Kruskal's theorem and the Feferman-Schütte ordinal.