# Definition:Continued Fraction/Simple/Infinite

## 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.