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"Almost all" in math can mean "except at every integer or fraction" :)
by jbaber 1y ago
"Almost all" in math can mean "except at every integer or fraction" :)
- layer8 1y agoThe semantics are almost always reasonable: https://en.wikipedia.org/wiki/Almost_all https://en.wikipedia.org/wiki/Almost_all
- tejtm 1y agoI would expect almost NO numbers are rational (integer or fraction) with an infinite number of Reals between each.
- JadeNB 1y ago> I would expect almost NO numbers are rational (integer or fraction) with an infinite number of Reals between each. You're right (technically correct, which is the best etc.)! That is why "almost all" can mean everything except rational numbers.
- noqc 1y agoin between any two real numbers, there is a rational number, and vice versa.
- concordDance 1y agoAnd yet somehow there are infinity times more reals than rationals... Very hard to get your head around!
- noqc 1y agoAn fun, immediate, horrifying, consequence. 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.
- JadeNB 1y ago> "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.)
- dullcrisp 1y agoSure 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.