Digitsequence

Digitsequence is a sequence consisting solely of decimal digits. Formally, it is a function from an index set to the digit set {0,1,2,3,4,5,6,7,8,9}, often denoted by a finite string of digits if the index set is finite, or an infinite sequence otherwise. In common usage, the term is synonymous with digit string or numeric string, especially when the sequence is finite.

Finite digit sequences are called digit strings; examples include "12345" or "007". Infinite digit sequences arise in mathematical constants such as the digits of pi: 3,1,4,1,5,9,2,6,5,...; or in numbers constructed by concatenation like the Champernowne constant 0.12345678910111213...

Operations on digitsequences include concatenation, indexing, and slicing. They are also commonly tested with regular expressions to verify digit-only content, for example using patterns like ^[0-9]+$, and they can be recognized by finite automata that accept digit-only inputs.

Applications of digitsequences appear in computing and mathematics. In computing, numeric strings are used for user input, identifiers, data encoding, and validation. In theory, digit sequences are studied in topics such as the distribution of digits, normal numbers, and randomness, as well as in constructions like constants formed by concatenating natural numbers.

Overall, a digitsequence provides a compact representation of decimal information and serves as a fundamental object across disciplines, enabling both practical data handling and theoretical analysis of decimal representations.