Impossible Event
In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one. The concept is analogous to the concept of "almost everywhere" in measure theory. While there is no difference between almost surely and surely (that is, entirely certain to happen) in many basic probability experiments, the distinction is important in more complex cases relating to some sort of infinity. For instance, the term is often encountered in questions that involve infinite time, regularity properties or infinite-dimensional spaces such as function spaces. Basic examples of use include the law of large numbers (strong form) or continuity of Brownian paths.
Almost never describes the opposite of almost surely; an event which happens with probability zero happens almost never.
Read more about Impossible Event: Formal Definition, "Almost Sure" Versus "sure", Asymptotically Almost Surely
Famous quotes containing the words impossible and/or event:
“The author’s hegemony must be broken. It is impossible to go too far in fanatical self-denial or fanatical self-renunciation: I am not I, but rather the street, the streetlights, this or that occurrence, nothing more. That’s what I call the style of stone.”
—Alfred Döblin (1878–1957)
“An event is not over until everyone is tired of talking about it.”
—Mason Cooley (b. 1927)