Definition:Continued Fraction/Simple/Infinite

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

A simple infinite continued fraction is a infinite continued fraction in $\R$ whose partial quotients 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 infinite continued fraction can be abbreviated SICF.

It is also known as a regular infinite continued fraction.

The order of the words can be varied, that is infinite simple continued fraction for example, but strives for consistency and does not use that form.

Also see

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