Definition:Length


 * Geometry:
 * Length (Linear Measure): a formal comparison between the spatial extent of a geometric figure in a specified direction against a reference quantity (often tacitly understood).


 * Analysis:
 * Length of (real) interval: the difference between the endpoints of a real interval.
 * Length of a curve: the limit of the length of a polygonal line inscribed within the curve as the maximum length of the chords which form that polygonal line tends to zero.


 * Complex Analysis:
 * Length (Complex Plane).


 * Set Theory:
 * Length of a Chain.
 * Length of a Sequence: the number of terms contained in a finite sequence.


 * Number Theory:
 * Length of Cycle of Periodic Continued Fraction.

Note that these two definitions are compatible with each other.
 * Graph Theory:
 * Length of a Walk: the number of edges in a walk (counting repeated edges as many times as they appear).
 * Length of a Branch: the number of ancestors of the leaf at the end of a branch of a rooted tree.


 * Logic and Formal Systems:
 * Length of a String: the number of symbols in a string.
 * Length of a Tableau Proof: the number of lines in a tableau proof.


 * Group Theory:
 * Length of an Orbit: The number of elements contained in the orbit of an element under a group action.
 * Length of a Normal Series: The number of factors in a normal series.
 * Length of a Group $G$: the length of a composition series for $G$.