# Definition:Continued Fraction/Simple/Infinite

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## 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 $a: \N_{\ge 0} \to \Z$ 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**.

The order of the words can be varied, that is **infinite simple continued fraction** for example, but $\mathsf{Pr} \infty \mathsf{fWiki}$ strives for consistency and does not use that form.

## Also see

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

## Sources

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