Definition:Continued Fraction/Simple

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Definition

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 $n > 0$.


Also known as

A simple continued fraction is also known as a regular continued fraction.

When the context is such that it is immaterial whether a simple continued fraction is finite or infinite, the abbreviation SCF can be used.


Also see

  • Results about simple continued fractions can be found here.


Sources