haggy

Coding Theory is used when sending messages over a channel with interference/noise. By incorporating sufficient "redundancy" in your messages you can ensure that the original message can be decoded/extracted even if a number of bits of information are lost during transmission of the message.

I think the point of the problem is the concept of the "base 3" number system. 1 = 3^0 3 = 3^1 9 = 3^2 27 = 3^3 Any number in base 10 will be able to be represented in base 3. E.g. 29 = 1*3^3 + 2*3^0 But 2*3^n = 1*3^(n+1) - 1*3^n, corresponding to putting the two weights on the opposite side of the scale.

Doron, don't you get tired proclaiming your ideas to those who don't care? You always point out others not understanding your methods of reasoning. Could it not be that you haven't expressed them in a concise and clear manner? I personally doubt that "professional mathematicians" don't understand your work due to their own limitations. You'd be surprised at their capabilities to consider complicated ideas. Don't come with that tripe about them not understanding included middle reasoning. In its purest state Set Theory comes very close to different types of philosophy, so those mathematicians that "don't understand" are likely to have seen errors in your work rather than been inadequate in their reasoning ability. How long are you going to harrass all and sundry with your ideas? Will it be until you get your own little following of people? Should we call them the "Doronians" as a fallback to the days of the Pythagoreans who couldn't accept that irrational numbers existed?

Dreamlord: 3.1415926535897932384626433832795... The whole "Bible Code" issue is quite boring. I know it's a repeated statement about Moby Dick also having such "hidden information" but just think about it, with a large enough text one can find many "patterns". With a large enough random text one could conceivably "extract" information .

But in terms of your description √1 isn't just the shadow of √2 it's also the shadow of 75, 89, 3.1415926535897932384626433832795 etc. Likewise √2 need not just be the shadow of √3 but also the shadow of any number you pick.

What exactly are you trying to show with √1 being "shadow" of √2, etc? By the same sort of illustration you could "show" √1, √2 to be the shadows of any number you please.

Let b[1] = c b[m] = c + d b[m^2] = c + 2d b[n] = c + Floor[Log_m[n]]*d b[n] = ?(1) + ?(lg n)

It could be a place for the Moderator to put those threads when they "pop up". Along with that "more valid" theories that aren't quite finished could be put there to gather feedback.

I think most of what would be posted there would be "PseudoMaths" but a lot of those who have their "AT's" don't consider it PseudoMaths.

I think an example of a thread I'd put into the "Alternative Theories" (AT) forum would be that of the "Limit and Infinity". That way learners would know what they were getting themselves into when looking through the thread. ed84c, I acknowledge that exposing people to new ideas wouldn't be too harmful but I think some threads merely make the water murkier for those learners, rather than broadening their horizons (in terms of knowledge/ideas). atinymonkey, I don't know if it would be an 'if you don't have a degree don't comment' forum. I think it could be a forum where threads could be along the lines of: . "I haven't quite finished proving XYZ, but what do you guys think" . "This is my new theory, it's contrary to (insert mainstream theory)" Some of the AT's are complete rubbish while others may be valid. This way "learners" could steer clear or delve into this "new territory" if they so wish.

So do you mean it doesn't matter what the values of a[n] are when m doens't divide n, as long as the property of it being an increasing sequence is maintained? If so, then isn't a[n] lower bounded by the sequence {b[n]} with b[n] defined as: b[n] = b[Floor[n/m]] + d In that case you could still use the Master Theorem Even if you don't want to use the master theorem, does that help at all?

As a new user I haven't been able to see how things have progressed at ScienceForums.net but I believe the users in the Maths forums mostly fall into a few categories: . Varsity Maths Students . Interested High School Students . Interested Members of the general public What I'm concerned about is the possibility of some people who have non-standard/alternative theories that use these forums to debate with those that are still learning what Maths is all about. What do you guys think about adding an extra forum for these alternative theories so that people viewing them know that they are a bit less "mainstream". I think this would ensure that the less "knowledgeable" aren't confused by things they really don't need to understand.

Where you have n/m are you meaning the floor/ceiling of n/m. If so, I think you can use the "Master Theorem". This gives asymptotic bounds.

Addition mod 2.

Ja, I know that. Just thought it might give someone else a better idea seeing as MandrakRoot's estimate was 0.086617. Suppose I should have said "converge" instead of leaving out the apostophes. Here's the Mathematica code if anyone's interested. G[x_] := IntegerDigits[2^x] A[n_] := Length[select[G[n], #1 > 4 &]] N[sum[A[n]/(2^n), {n, 0, 2000}], 50] If anyone can see an error please tell me.

When I worked it out it converged to ~ 2/9. Merely calculated the sum of the first 2000 terms.