# Category:Simple Continued Fractions

This category contains results about **Simple Continued Fractions**.

Definitions specific to this category can be found in **Definitions/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 $n > 0$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Simple Continued Fractions"

The following 24 pages are in this category, out of 24 total.

### C

- Continued Fraction Expansion of Limit of Simple Infinite Continued Fraction equals Expansion Itself
- Convergents of Simple Continued Fraction are Rationals in Canonical Form
- Correspondence between Irrational Numbers and Simple Infinite Continued Fractions
- Correspondence between Rational Numbers and Simple Finite Continued Fractions