# Definition:Continued Fraction/Simple/Finite

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## 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.