Continuous group

A continuous group, in mathematics, is a collection of objects called transformations or symmetries that can be smoothly and infinitely varied. Imagine rotating an object around a fixed point; you can rotate it by any degree, not just specific fixed angles. These groups are called continuous because their elements change in small, seamless steps rather than sudden jumps. They are fundamental in understanding how objects can be symmetrically transformed, such as rotations, translations, or scaling, and are essential in fields like physics and geometry for analyzing systems with smooth symmetries.