A sequence x (i.e. a function x mapping N to a metric space S) is said to diverge if for every positive real number M, |x(n)| < M for only finitely many natural numbers n. Any unbounded sequence clearly diverges.

Di*verge" (?), v. i. [imp. & p. p. Diverged (?); p. pr. & vb. n. Diverging.] [L. di- = dis- + vergere to bend, incline. See Verge.]


To extend from a common point in different directions; to tend from one point and recede from each other; to tend to spread apart; to turn aside or deviate (as from a given direction); -- opposed to converge; as, rays of light diverge as they proceed from the sun.


To differ from a typical form; to vary from a normal condition; to dissent from a creed or position generally held or taken.


© Webster 1913.

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