zeroone

Zeroone, sometimes written zero-one or 0-1, refers to the two binary values 0 and 1 that form the basis of digital computation and Boolean logic. In computing, binary digits—bits—are used to encode information, perform logic operations, and build data representations. The term also appears in mathematical and statistical contexts where the values 0 and 1 represent false/true, off/on, or absence/presence.

In probability theory, the zero-one law describes events whose probability is either zero or one. These are typically tail events determined by an infinite sequence of independent random variables; such laws imply that certain asymptotic properties are almost surely determined by the remote past.

In statistics and machine learning, the zero-one loss is the simplest error measure for classification. It assigns a value of 1 when a prediction is incorrect and 0 when it is correct. Although intuitive, the zero-one loss is not convex, making optimization challenging; surrogate losses are often used in training.

In the study of sorting networks and Boolean functions, the zero-one principle states that if a network or circuit correctly sorts all sequences of 0s and 1s, it will correctly sort any finite sequence of numbers. This principle reduces analysis to binary inputs.

Beyond theory, zeroone or zero-one appears in branding and product names, reflecting the binary duality at the heart of modern computation. See also: binary digit, boolean algebra, zero-one law, zero-one loss.