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You are not logged in. #1 20060727 12:04:40
Prove It!Prove that any positive integer can be expressed as a sum of terms in the Fibonacci sequence without using any term more than once. You can shear a sheep many times but skin him only once. #2 20060810 01:27:09
Re: Prove It!Great question. I've never tried this before, so here goes nothing: If you don't understand this, or induction proofs in general, let me know. This proof also outlines how you should come up with such summations. We can do 1 to 5 by: 1: 1 2: 1 + 1 3: 2 + 1 4: 3 + 1 5: 3 + 2 Now we want to go from 5 to 8. All we do is take our first 3, and add 5 to them. We can do this since we know 5 can't be in any of them (since they are less than 5): 6: 5 + 1 7: 5 + 1 + 1 8: 5 + 2 + 1 Now we can do the same thing to get to 13: 9: 8 + 1 10: 8 + 1 + 1 11: 8 + 2 + 1 12: 8 + 3 + 1 13: 8 + 3 + 2 And by the proof above, this must work for all numbers. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20060810 08:43:00
Re: Prove It!Ricky, your LaTeX goes off the page, you might want to make it easier to read. Otherwise, everything looks good. #4 20060810 10:34:59
Re: Prove It!I think that has to do with your screen resolution. Try changing it and see if it helps. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #5 20060810 11:30:04
Re: Prove It!I can't get it any better on this monitor . I wonder if there is a way to make LaTeX work for everyone's point of view. Equations will wrap, why doesn't \mbox{}? #6 20060824 08:15:00
Re: Prove It!The latex goes the page indeed. IPBLE: Increasing Performance By Lowering Expectations. #7 20060824 08:20:00
Re: Prove It!And there's more generalized result: Zeckendorf's theorem Last edited by krassi_holmz (20060824 08:20:40) IPBLE: Increasing Performance By Lowering Expectations. 