In Americaalone, peoplespent $170 billion on “direct marketing”—junk mail of both the physical and electronic varieties—last year. Yet of those who receivedunsolicitedadverts through the post, only 3% boughtanything as a result. If the bumf arrivedelectronically, the take-uprate was 0.1%. And for onlineadverts the “conversion” into sales was a minuscule 0.01%. That meansabout $165 billion was spentnot ondrummingupbusiness, but on annoyingpeople, creatinglandfill and clutteringspamfilters.
The collection of cofinite subsets of ℝ is a filterunder inclusion: it includes the intersection of everypair of its members, and includesevery superset of every cofinite set.
If (1) the universal set (here, the set of natural numbers) were called a "large" set, (2) the superset of any "large" set were also a "large" set, and (3) the intersection of a pair of "large" sets were also a "large" set, then the setof all "large" sets would form a filter.