Mathematical groups

A mathematical group is a set of elements combined with an operation, like addition or multiplication, that satisfies four key properties: closure (any two elements combined produce another within the set), associativity (the way you group operations doesn’t change the result), an identity element (a special element that doesn’t change others when combined), and inverses (for every element, there's another that neutralizes it). Groups are fundamental in understanding symmetry, structure, and patterns across mathematics and science, providing a unified way to analyze systems with consistent, reversible interactions.