Cycle (mathematics)
In mathematics, and in particular in group theory, a cycle is a permutation of the elements of some set X which maps the elements of some subset S of X to each other in a cyclic fashion, while fixing (i.e., mapping to themselves) all other elements of X. For example, the permutation of {1, 2, 3, 4} that sends 1 to 3, 2 to 4, 3 to 2 and 4 to 1 is a cycle, while the permutation that sends 1 to 3, 2 to 4, 3 to 1 and 4 to 2 is not (it separately permutes the pairs {1, 3} and {2, 4}). The set S is called the orbit of the cycle.
Read more about Cycle (mathematics): Definition, Basic Properties, Transpositions
Famous quotes containing the word cycle:
“The lifelong process of caregiving, is the ultimate link between caregivers of all ages. You and I are not just in a phase we will outgrow. This is life—birth, death, and everything in between.... The care continuum is the cycle of life turning full circle in each of our lives. And what we learn when we spoon-feed our babies will echo in our ears as we feed our parents. The point is not to be done. The point is to be ready to do again.”
—Paula C. Lowe (20th century)