concatenating

Concatenating, or concatenation, is the operation of joining two or more sequences end-to-end to form a new sequence that contains the elements of the originals in their original order. The result typically has a length equal to the sum of the lengths of the inputs. Concatenation is a common operation in mathematics and computer science and applies to strings, arrays, lists, or other sequences.

In mathematics and formal languages, concatenation applies to finite or infinite sequences. The operation is associative: (xy)z = x(yz). The empty sequence serves as an identity element. Notation varies by domain, but juxtaposition or a dedicated operator is common. For example, concatenating the strings "ab" and "cd" yields "abcd".

In computer science, concatenation is frequently used for strings and lists. Many programming languages provide a concatenation operator or function, such as the plus operator in several languages or dedicated methods. Strings are often immutable, so repeated concatenation can create intermediate copies and impact performance; this is mitigated by builders, join functions, or streaming approaches in practice. Examples: Python: "Hello" + "World" → "HelloWorld"; Java: "Hello" + "World" → "HelloWorld" (often optimized behind the scenes); JavaScript: "Hello" + " " + "World" → "Hello World". Lists or arrays can be concatenated in a similar way, producing a new sequence.

Other domains include databases, where SQL provides CONCAT to assemble field values, and shell or file processing, where concatenation combines contents or strings. Important considerations include encoding for strings, handling of delimiters, and clarifying when concatenation is distinct from a join or merge operation.