Denominators of Simple Continued Fraction are Strictly Positive

Theorem
Let $n \in \N \cup \{\infty\}$ be an extended natural number.

Let $(a_0, a_1, \ldots)$ be a simple continued fraction in $\R$ of length $n$.

Let $q_0, q_1, q_2, \ldots$ be its denominators.

Then for $0 \leq k \leq n$ we have $q_k > 0$.

Proof
Follows from:
 * $q_0 = 1$ by definition
 * Denominators of Simple Continued Fraction are Strictly Increasing