loop

Loop is a term used in many fields to describe a closed path or a repeating sequence. In common usage, a loop refers to something that returns to its starting point or cycles indefinitely.

In abstract algebra, a loop is a set with a binary operation that has an identity element and unique inverses for every element, but unlike a group, the operation need not be associative. Loops generalize groups and include structures such as Moufang loops and Bol loops.

In geometry and topology, a loop is a closed curve in a space. In algebraic topology, a based loop is a continuous map from the circle to a space that preserves a designated base point; the collection of all based loops forms a loop space, which is important in the study of homotopy and fundamental groups.

In programming, a loop is a control structure that repeats a block of code while a condition holds. Common forms include for loops, while loops, and do-while loops. Loops enable iteration, but faulty conditions can cause infinite loops, where the block runs without end.

In music and digital audio, a loop is a short section of sound or a musical phrase that repeats to form a longer composition. Looping is widely used in electronic music and in live performances via loop pedals or software.

In systems theory and engineering, a feedback loop is a mechanism where part of a system’s output is returned to influence future output. Negative feedback tends to stabilize systems, while positive feedback can amplify changes and lead to oscillations or instability.