Prove that any number \(x \in \mathbb{N} \) can be represented uniquely by the sum of unique Fibonacci numbers that are NOT consecutive.

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Prove that any number \(x \in \mathbb{N} \) can be represented uniquely by the sum of unique Fibonacci numbers that are NOT consecutive.

Mathematics
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This is a thing?
I guess it gives it away to say this is called Zeckendorf's theorem. Rofl I just discovered this and thought it sounded cool.
Things that are on my mind right now: - Induction - Creating various independent sequences of numbers that have no term in common and also that their union is \(\mathbb N\)

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Let's just try to figure out this proof together here: https://en.wikipedia.org/wiki/Zeckendorf's_theorem#Proof
Oh, great. I got the induction thing right.
I feel like understanding how someone could prove such a crazy statement as this would lead us to understanding some pretty interesting stuff haha.
Strong-induction is really mind-boggling. It's amazing how well it works if you don't know how to prove things.
How did they even come up with that proof? The uniqueness one is even worse.
-.-
Yeah this is pretty much too crazy for me, I wonder if numberphile did a video on this or if there's a youtube video of someone explaining it to me
Math is cool.

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