A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Empty

  • one year ago

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

  • This Question is Closed
  1. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    This is a thing?

  2. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I guess it gives it away to say this is called Zeckendorf's theorem. Rofl I just discovered this and thought it sounded cool.

  3. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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 \(\mathbb N\)

  4. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Let's just try to figure out this proof together here: https://en.wikipedia.org/wiki/Zeckendorf's_theorem#Proof

  5. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh, great. I got the induction thing right.

  6. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I feel like understanding how someone could prove such a crazy statement as this would lead us to understanding some pretty interesting stuff haha.

  7. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Strong-induction is really mind-boggling. It's amazing how well it works if you don't know how to prove things.

  8. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    How did they even come up with that proof? The uniqueness one is even worse.

  9. ikram002p
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -.-

  10. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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

  11. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Math is cool.

  12. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.