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.
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...
(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...
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...
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...
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.
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...
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...