Restricted Partial Quotients

Restricted Partial Quotients

In mathematics, and more particularly in the analytic theory of regular continued fractions, an infinite regular continued fraction x is said to be restricted, or composed of restricted partial quotients, if the sequence of denominators of its partial quotients is bounded; that is

and there is some positive integer M such that all the (integral) partial denominators ai are less than or equal to M.

Read more about Restricted Partial Quotients:  Periodic Continued Fractions, Restricted CFs and The Cantor Set, See Also

Famous quotes containing the words restricted and/or partial:

    Love is like some fresh spring, first a stream and then a river, changing its aspect and its nature as it flows to plunge itself in some boundless ocean, where restricted natures only find monotony, but where great souls are engulfed in endless contemplation.
    HonorĂ© De Balzac (1799–1850)

    The one-eyed man will be King in the country of the blind only if he arrives there in full possession of his partial faculties—that is, providing he is perfectly aware of the precise nature of sight and does not confuse it with second sight ... nor with madness.
    Angela Carter (1940–1992)