Value of Finite Continued Fraction of Strictly Positive Real Numbers is Strictly Positive

Theorem

Let $\sequence {a_0, \ldots, a_n}$ be a finite continued fraction in $\R$ of length $n \ge 0$.

Let all partial denominators $a_k > 0$ be strictly positive.

Let $x = \sqbrk {a_0, a_1, \ldots, a_n}$ be its value.

Then $x > 0$.

Proof

This theorem requires a proof. In particular: use Definition:Value of Continued Fraction You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Also see

• Properties of Value of Finite Continued Fraction