1containing

1containing is an informal term used in mathematics and computer science to describe objects that include the digit 1 in a standard representation. The term is not widely standardized, but in practice it appears in puzzles, data analysis, and string-processing contexts to denote a property of having at least one occurrence of the symbol 1.

In number theory, a positive integer is 1containing if its decimal representation contains the digit 1 at least once. For example, 101 and 42 contain 1, while 200 does not. If one considers all k-digit numbers, the fraction that are 1containing is 1 − (9/10)^k; as k increases, this fraction approaches 1.

In string processing, a string is 1containing when the character '1' appears anywhere in the string. This concept is used in pattern matching, filtering, and validation tasks where the presence of the digit or symbol is a condition.

Other uses extend the idea to arrays, matrices, or data sets that contain at least one element equal to 1. In database queries, a 1containing criterion might select records with a field equal to 1.

See also digit, contains, pattern matching, and digit density.