Fibonacci seed at index zero

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The standard Fibonacci sequence begins with F₀=0. Together with F₁=1 and the additive recurrence, this fixes every later term. It also means a ratio with F₀ in the denominator is undefined.

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Original context

with conjugate $\golden^{-1} = \golden - 1 \approx 0.618033988749895$.
\end{definition}

\begin{definition}[Fibonacci Sequence]
$\fib{0} = 0$, $\fib{1} = 1$, and $\fib{n} = \fib{n-1} + \fib{n-2}$ for $n \geq 2$.
\end{definition}

The ratio of consecutive Fibonacci numbers converges to $\golden$:
\begin{equation}
\lim_{n \to \infty} \frac{\fib{n}}{\fib{n-1}} = \golden
\end{equation}

\fib{0} = 0

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