 Invariant (mathematics)

An invariant is a property or quantity unchanged by a specified class of transformations. The transformations are part of the definition: an invariant of a group action and an invariant set of a measure-preserving transformation concern different transformation classes.

In mathematics, an **invariant** is a property or quantity that remains unchanged under certain transformations or operations. The concept of invariance is fundamental in various fields of mathematics, including algebra, geometry, calculus, and topology. Here are some key areas where invariants are commonly discussed: 1. **Geometry**: Invariants under geometric transformations (like translations, rotations, and reflections) could include properties like distances, angles, or areas.