Definition:Continued Fraction/Simple/Finite

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

Let $n \ge 0$ 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 $a: \closedint 0 n \to \Z$ 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.

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

Also see