**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 *a _{i}* 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:

“Language can only deal meaningfully with a special, *restricted* segment of reality. The rest, and it is presumably the much larger part, is silence.”

—George Steiner (b. 1929)

“We were soon in the smooth water of the Quakish Lake,... and we had our first, but a *partial* view of Ktaadn, its summit veiled in clouds, like a dark isthmus in that quarter, connecting the heavens with the earth.”

—Henry David Thoreau (1817–1862)