I feel like this is a difference between “almost surely” and “surely”, both of which are typically expressed as “probability 1”, but which are qualitatively different. I’m wondering whether infinitesimals would actually work to represent “almost surely” as 1−ϵ (as suggested in this post).
Also a nitpick and a bit of a tangent, but in some cases, a mathematician will accept any probability > 1 as proof; probabilistic proof is a common tool for non-constructive proof of existence, especially in combinatorics (although the way I’ve seen it, it’s usually more of a counting argument than something that relies essentially on probability).
I feel like this is a difference between “almost surely” and “surely”, both of which are typically expressed as “probability 1”, but which are qualitatively different. I’m wondering whether infinitesimals would actually work to represent “almost surely” as 1−ϵ (as suggested in this post).
Also a nitpick and a bit of a tangent, but in some cases, a mathematician will accept any probability > 1 as proof; probabilistic proof is a common tool for non-constructive proof of existence, especially in combinatorics (although the way I’ve seen it, it’s usually more of a counting argument than something that relies essentially on probability).