# Definition:Continued Fraction/Simple/Infinite

## Contents

## Definition

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

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

That is, it is a sequence $a : \N_{\geq 0} \to \Z$ with $a_n > 0$ for $n >0$.

## Also known as

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

## Also see

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

## Sources

- Weisstein, Eric W. "Simple Continued Fraction." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/SimpleContinuedFraction.html