continuousdigit

continuousdigit refers to a mathematical concept related to the properties of numbers, particularly in the context of their decimal or other positional representations. It is not a universally defined term with a single, standard meaning in mainstream mathematics. However, when the term is used, it generally implies a number whose digits exhibit a specific pattern or continuity, often in a non-repeating and non-terminating manner.

One interpretation could be a number formed by concatenating digits in a way that suggests a continuous progression or sequence, such as the Champernowne constant, which is formed by concatenating all positive integers in order: 0.123456789101112... This number is transcendental and normal in every integer base.

Another possible meaning could relate to numbers where the digits change in a predictable, albeit not necessarily arithmetic or geometric, fashion. This might arise in the study of chaotic systems or fractal sets where the generation of digits follows complex rules. The concept is distinct from repeating decimals, which have a predictable, finite pattern of digits, or terminating decimals, which have a finite number of non-zero digits. The essence of "continuousdigit" lies in a potentially infinite and non-obvious, yet structured, progression of numerical values in its representation.