Randomness

Randomness is the lack of pattern or predictability in events. A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events (or "trials") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy.

The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.

Fact

A fact is something that has really occurred or is actually the case. The usual test for a statement of fact is verifiability—that is, whether it can be demonstrated to correspond to experience. Standard reference works are often used to check facts. Scientific facts are verified by repeatable careful observation or measurement (by experiments or other means).

Etymology and usage

The word fact derives from the Latin factum, and was first used in English with the same meaning: a thing done or performed, a meaning now obsolete. The common usage of "something that has really occurred or is the case" dates from the middle of the sixteenth century.

Fact is sometimes used synonymously with truth, as distinct from opinions, falsehoods, or matters of taste. This use is found in such phrases as, "It is a fact that the cup is blue" or "Matter of fact", and "... not history, nor fact, but imagination." Filmmaker Werner Herzog distinguishes clearly between the two, claiming that "Fact creates norms, and truth illumination."