I spun up a quick survey[1] that I sent out to friends and family to try to get some numbers on these sorts of phrases. Results so far are inconclusive.
If there's a finite subset of an infinite set, almost all members of the infinite set are not in the finite set. E.g. Almost all integers are not 5: the set of integers equal to five is finite and the set of integers not equal to five is countably infinite.
Likewise for two infinite sets of different size: Almost all real numbers are not integers.
Etc.
You're right (technically correct, which is the best etc.)! That is why "almost all" can mean everything except rational numbers.
Very hard to get your head around!
If I remove n elements from R, the remainder has n+1 connected components.
The complement of Z in R has |Z| connected components.
The complement of Q in R has |R| connected components.
I am a mathematician, but, even so, I think that this is one of those instances where we have to admit that we have mangled everyday terminology when appropriating it, and so non-measure theoretic users should just ignore our definition. (Similarly with "group," where, at the risk of sounding tongue-in-cheek because it's so obvious, if I were trying to analyze how people usually understand its everyday meaning I wouldn't include the requirement that every element have an inverse.)