Discrete groups

Discrete groups are mathematical structures consisting of a set of elements combined with an operation (like addition or multiplication) that satisfies certain rules. "Discrete" means the elements are separate and distinct, with no continuous flow between them. An example is the set of integers under addition; they form a discrete group because you can move from one to another in steps, rather than continuously. These groups are fundamental in understanding symmetry, patterns, and structure in mathematics and physics, as they capture the idea of separate, countable transformations or arrangements.