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  1. rumborak

    I The Weierstrass function's' odd qualities

    Oooh, that is an excellent explanation, thanks a lot. It's been a long time since college math, I had forgotten that a "kink" in a graph is non-differentiable. From there it's not too hard to construct an "only kinks" function.
  2. rumborak

    I The Weierstrass function's' odd qualities

    I recently stumbled on the Weierstrass function, whose main claim to fame (as I understand it) is to be continuous everywhere, but non-differentiable everywhere as well. Apparently I was in good company with Gauss' and others who assumed that to be impossible! I guess I'm asking, is this...
  3. rumborak

    I Why are "irrational" and "transcendental" so commonly used to describe numbers

    (sorry, the thread title got mangled. It should be "why are irrational and transcendental so commonly used to describe numbers") Is this simply out of the most common ways of how one would try to describe a number? (e.g. first try ratios, then polynomials) Or is there a deeper reason for this...
  4. rumborak

    B Penrose' Chess problem

    I have read several books by Penrose, including the brilliant Road to Reality, but yes, he is both bizarrely brilliant, and bizarrely simplistic in his understanding of certain matters. In fact, his attempts to inject theology into unrelated topics often serve as a good reminder that brilliant...
  5. rumborak

    I A simple theorem we pondered in our ski lodge... (sum of Fibonacci numbers)

    Awesome, thanks. I figured there would be some ancient proof of this. 1970s is surprisingly young actually!
  6. rumborak

    I A simple theorem we pondered in our ski lodge... (sum of Fibonacci numbers)

    We talked about Fibonacci numbers, and I wondered: Can any natural number be construed by a sum of unique Fibonacci numbers? My guess was yes, and a C program I wrote confirms that to be up to about 2,000, but that's of course is no proof. The best semi-proof I could come up with is that the...
  7. rumborak

    Is this an integer programming problem?

    Thanks everybody. While (as it so often is) it didn't "solve" my programming problem, it definitely made me understand the problem space much better now.
  8. rumborak

    Is this an integer programming problem?

    Hmm, that's an interesting idea (and somehow it feels similar to Common Denominator calculation), but sadly my example used simple values for 'a' for illustrative purposes, not because they are actually constrained to it. So, the 'a's should be considered real numbers, e.g. 1.7853467 etc. Maybe...
  9. rumborak

    Is this an integer programming problem?

    At work I am writing a somewhat complex piece of software, and inside it at some point I have to solve the following problem: I have several "streams", each of which has equally spaced points according to a proportionality factor 'a', i.e. X=a*n. Each stream has a different 'a'. As an example...
  10. rumborak

    Infinity vs Transfinite?

    Err, did you actually click on the link? Your question is answered right in the first sentence of that article.
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