We prove that almost no numbers in Cantor's middle-thirds set are very well approximable by rationals. More generally, we discuss Diophantine properties of almost every point, where 'almost every' is ...

Without the theorem of the excluded middle, all kinds of difficulties arise. In fact, many mathematical proofs are based on ...

More precisely, we prove that if the sum of the Hausdorff dimensions of two regular Cantor sets is bigger than one then, in almost all cases, there are translations of them whose intersection ...