Definition:Continued Fraction/Simple/Finite

Definition
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 strives for consistency and does not use that form.

Also see

 * Definition:Value of Finite Continued Fraction
 * Definition:Simple Infinite Continued Fraction
 * Correspondence between Rational Numbers and Simple Finite Continued Fractions