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:
“It is almost impossible to be a doctor and an honest man, but it is obscenely impossible to be a psychiatrist without at the same time bearing the stamp of the most incontestable madness: that of being unable to resist that old atavistic reflex of the mass of humanity, which makes any man of science who is absorbed by this mass a kind of natural and inborn enemy of all genius.”
—Antonin Artaud (1896–1948)
“Don’t you go believing in sayings, Picotee: they are all made by men, for their own advantages. Women who use public proverbs as a guide through events are those who have not ingenuity enough to make private ones as each event occurs.”
—Thomas Hardy (1840–1928)