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’s impossible to speak what it is not noble to do.”
—Sophocles (497–406/5 B.C.)
“We can glut ourselves with how-to-raise children information . . . strive to become more mature and aware but none of this will spare us from the . . . inevitability that some of the time we are going to fail our children. Because there is a big gap between knowing and doing. Because mature, aware people are imperfect too. Or because some current event in our life may so absorb or depress us that when our children need us we cannot come through.”
—Judith Viorst (20th century)