Contractions on belief sets that have no finite representation cannot be finite in the sense that only a finite number of sentences is removed. However, such contractions can be delimited so that the ...

With a surprising new proof, two young mathematicians have found a bridge across the finite-infinite divide, helping at the same time to map this strange boundary. The boundary does not pass between ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...