Note: although the phrase “almost all” sounds like an intuitive English-sentence idea, it actually has a very precise mathematical meaning: it means the complem

Note: although the phrase “almost all” sounds like an intuitive English-sentence idea, it actually has a very precise mathematical meaning: it means the complement has Lebesgue measure zero. It sounds like maybe you take issue with this phrase. I kind of think about it probabilistically: if you start uniformly sampling decimal digits 0-9 at random d1,d2,d3,… then the corresponding number 0.d1d2d3… (with the digits going on forever) will be irrational with probability 1.