3 ms·
Remember coming across this concept while reading about Measure theory. There are also concepts like "almost well-ordered" and "almost complete" in graph theory
by yantrams 8y ago
Remember coming across this concept while reading about Measure theory. There are also concepts like "almost well-ordered" and "almost complete" in graph theory if my memory serves right.
- anyfoo 8y agoSomething applying to “almost all” elements in a (preferably infinite) set: Applies to all elements, with the exception of a finite number of elements. For example, almost all prime numbers are odd.
- yantrams 8y agoExactly! I can't remember where but I distinctly remember some theory quantifying this as almost-1, almost-2,... as a function of the number of finite (or countably infinite maybe) exceptions.
- jhanschoo 8y agoA warning: in general mathematical usage, this is not the definition of "almost all"; the notion of "almost all" is with respect to some notion of measure on a set. In the set of real numbers, for example, with the usual Lebesgue measure on it, if all but a /countable/ number of elements has a property X, then almost all the reals has that property X. (Note that uncountable sets in R exists that have zero measure; i.e. uncountable sets that "almost no" points in R lie in that uncountable subset of R)
- anyfoo 8y agoAh. "With the exception of finitely many" [1] was the definition given to me in University. The generalization makes sense, however. [1] I don't think I'm doing a good job translating the original German definition I was given, which sounds much better: "Mit Ausnahme endlich vieler".
- jhanschoo 8y agoAh, in English "all but finitely many" is indeed very commonly used, and rarely is "almost all" defined to have that sense.