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by SAI_Peregrinus
411 days ago
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"Almost all" is an interesting one, because it has family of mathematical definitions in addition to any informal definitions. If X is a set, "almost all elements of X" means "all elements of X except those in a negligible subset of X", where "negligible" depends on context but is well-defined. 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. |
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