# Definition:Continued Fraction/Simple/Finite

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## Contents

## Definition

Let $\R$ be the field of real numbers.

Let $n\geq 0$ be a natural number.

A **simple finite continued fraction of length $n$** is a finite continued fraction in $\R$ of length $n$ whose partial quotients are integers that are strictly positive, except perhaps the first.

That is, it is a finite sequence $a : \left[0 \,.\,.\, n\right] \to \Z$ with $a_n > 0$ for $n >0$.

## Also known as

A **simple finite continued fraction** can be abbreviated **SFCF**. It is also known as a **regular finite continued fraction**.

## Also see

- Definition:Value of Finite Continued Fraction
- Definition:Infinite Simple Continued Fraction
- Correspondence between Rational Numbers and Simple Finite Continued Fractions

## Sources

- Weisstein, Eric W. "Simple Continued Fraction." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/SimpleContinuedFraction.html - 1963: C.D. Olds:
*Continued fractions*: $\S$ $1.2$: Definitions and Notation