However, a discrete symmetry can always be reinterpreted as a subset of some higher-dimensional continuous symmetry, e.g. reflection of a 2-dimensional object in 3-dimensional space can be achieved by continuously rotating that object 180 degrees across a non-parallel plane.
For most practical purposes, continuous symmetry is modelled by a group action of a topological group that preserves some structure.
The simplest motions follow a one-parameter subgroup of a Lie group, such as the Euclidean group of three-dimensional space.
For example translation parallel to the x-axis by u units, as u varies, is a one-parameter group of motions.
The search for continuous symmetries only intensified with the further developments of quantum field theory.