Ciro Santilli @cirosantilli 35

The size of a set.

For finite sizes, the definition is simple, and the intuitive name "size" matches well.

But for infinity, things are messier, e.g. the size of the real numbers is strictly larger than the size of the integers as shown by Cantor's diagonal argument, which is kind of what justifies a fancier word "cardinality" to distinguish it from the more normal word "size".

The key idea is to compare set sizes with bijections.

No open signup it seems. TODO CV of owner.

They are making a proof assistant to integrate into the website: github.com/bookofproofs/fpl/, reminds Ciro Santilli of website front-end for a mathematical formal proof system.

It's just too charming, and has some deep themes.

Not possible it seems:

Subtle is the Lord by Abraham Pais (1982) chapter 4 "Entropy and Probability" mentions well how Boltzmann first thought that the second law was an actual base physical law of the universe while he was calculating numerical stuff for it, including as late as 1872.

But then he saw an argument by Johann Joseph Loschmidt that given the time reversibility of classical mechanics, and because they were thinking of atoms as classical balls as in the kinetic theory of gases, then there always exist a valid physical state where entropy decreases, by just reversing the direction of time and all particle speeds.

So from this he understood that the second law can only be probabilistic, and not a fundamental law of physics, which he published clearly in 1877.

It is not a practical fighting style. But it is an awesome game/exercise.

TODO why it is optimal: physics.stackexchange.com/questions/149214/why-is-the-carnot-engine-the-most-efficient

cat-v.org/ by Rob Pike, co-creator of Go, looong time Unixer, and some kind of leader of a 9p resurrection cult. That one's spicy. E.g.: harmful.cat-v.org/, Ciro's version: good and evil.