> "Almost all" in math can mean "except at every integer or fraction" :)

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.)

I would expect almost NO numbers are rational (integer or fraction) with an infinite number of Reals between each.

The semantics are almost always reasonable: https://en.wikipedia.org/wiki/Almost_all

Sure but that’s because 100% of real numbers, by any standard measure, aren’t integers or fractions. It bothers me if it’s used to mean 95% of something though.