Category:Definitions/Simple Continued Fractions

This category contains definitions related to Simple Continued Fractions.
Related results can be found in Category:Simple Continued Fractions.

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

Simple Finite Continued Fraction

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 denominators 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 $n > 0$.

Simple Infinite Continued Fraction

A simple infinite continued fraction is a infinite continued fraction in $\R$ whose partial denominators 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 $n > 0$.