Definition:Continued Fraction/Simple/Infinite

Definition
Let $a_1, a_2, a_3, \ldots \in \Z_{>0}$ be strictly positive integers.

Then the expression:


 * $a_1 + \cfrac 1 {a_2 + \cfrac 1 {a_3 + \cfrac 1 {\ddots \cfrac {} {a_{n - 1} + \cfrac 1 {a_n + \cfrac 1 {\ddots} } } } } }$

is a simple infinite continued fraction.

That is, a simple infinite continued fraction is an infinite continued fraction whose partial quotients are all strictly positive integers.

A simple infinite continued fraction can be abbreviated SICF.