 However, many applications of probability require what are known as continuous distributions (such as the uniform/rectangular, normal, and beta distributions), and thus require a restriction to countable additivity. In a continuous distribution, there are uncountably many states, usually named by real numbers. Each individual state has probability 0, even though events containing uncountably many states often have non-zero probability. (This violates full additivity.) However, in the common continuous distributions, there is usually a way to define a probability density for each state, such that the probability of any event is the integral of the density over the states that make it up. In finite and discrete distributions, it is standard to treat events of probability 0 as if they do not happen, while in continuous distributions there is always some event of probability 0 that occurs.