Fibonacci series is an infinite sequence of integers, starting with $1$ and $2$ and defined recursively after that, for the $n$th term in the array, as $F(n) = F(n-1) + F(n-2)$. How is the countability of Fibonacci sequence proven?
2026-02-22 21:58:58.1771797538
Countability of Fibonacci series
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A set $S$ is countable iff there exists a bijection between $\mathbb{N}$ and $S$
This means that we have to find that bijection, and as the Fibonacci Numbers is a subset of $\mathbb{N}$, it must be countable. Or stated differently, we could just map a number $n$ to the $n$th fibonacci number.