"Almost Sure" Versus "sure"
The difference between an event being almost sure and sure is the same as the subtle difference between something happening with probability 1 and happening always.
If an event is sure, then it will always happen, and no outcome not in this event can possibly occur. If an event is almost sure, then outcomes not in this event are theoretically possible; however, the probability of such an outcome occurring is smaller than any fixed positive probability, and therefore must be 0. Thus, one cannot definitively say that these outcomes will never occur, but can for most purposes assume this to be true.
Read more about this topic: Impossible Event
Famous quotes containing the word sure:
“I know nothing which life has to offer so satisfying as the profound good understanding, which can subsist, after much exchange of good offices, between two virtuous men, each of whom is sure of himself, and sure of his friend. It is a happiness which postpones all other gratifications, and makes politics, and commerce, and churches, cheap.”
—Ralph Waldo Emerson (1803–1882)