Unity+

Kerosene: And the chemical formula presents as: [math]26H_{2}O+12CO_{2}+catalyst=C_{12}H_{26}[/math](needs correcting?). So, I think it is possible.

And then there are the theory builders that also do problem solving.

The reason why properties, with slight changes, mainly remain the same because even with a change of base the actions stay similar and seem similar in many cases. You can correct me on this though.

Derivatives of all orders seems to be the one I'm talking about.

I'm talking about where between [a, b], is the curve not "smooth"(where it follows a parabolic curve in a sense) or does it contain more wave-like structures? Here is an example: The problem with this and using the method of taking derivatives is if there is any point on the curve so minuscule, yet there is an irregularity then it may take a long time to detect this if it even exists on the curve. There was this: http://en.wikipedia.org/wiki/Smooth_function, but it didn't seem to be the same kind of smoothness.

I can rewrite it in binary, yes. So, 1/3 = .333... which, in binary, is .0101010101... .0101010101... + .0101010101... = .10101010...(.666...). .0101010101...+ .10101010... = .111111111...(.999... = 1).

Given a function f(x) that is not a regular polynomial equation(x^n +/- x^n-1 +/- x-2...), how would one determine if a function is smooth over a curve or not? For example, let us say there is a given function that has a curve involved. Given the conditions above, how would one determine if all the parts of the curve are smooth in the sense that there are no other irregular curves on that curve even at the most minuscule spot of the curve?

It also goes along to proving that .9999... is equal to 1. We know that 1/3 equals .333.. and 3*1/3= 1 There is also other proofs of this, such as 1/9 = .1111... and 1/9 * 9 = 9/9 and .999..... Therefore, a similarity between those two proofs is 1/3^n * 3^n = 1. EDIT: Breaking this down, 1/n^s * n^s = 1.

But what I have been trying to get at is taking algorithms that are already possible to do and use the function at discussion to find another algorithm that is more efficient.

EDIT: Why would it be a contradiction in terms? The whole point is to find a possible algorithms given a particular algorithm that solves a particular task.

Well, one task I would have in mind would be finding the prime components of a number that is made up of two large prime numbers or other problems related to the P v NP problem.

Well, post when you have got something.

Well, the idea also goes along the philosophy of "with such simple rules, there are complex results. With complex rules, there are simplistic results." In fact, this idea has brought me to open this topic again to discussion. Though my original idea was flawed, I think there are some corrections that can be made to it. Though this is generally true, it is not always true. EDIT: Adding onto this... Could you give more detail onto why this is true? I want to have a list of ideas and restrictions that could lead to another idea I have. One flaw that existed within the idea was assuming that we are dealing with an axiom rather than a theorem or set of processes. Instead, the focus should be on determining what set of axioms that process or algorithm rests in first, if that makes sense. That is more a human problem rather than a problem with the amount of ideas that exist for a solution. When a process has been found for finding an idea, we generally stick to processes that lie within the range of the original process found because we find that processes that lie in range of the original will work best.

This is a problem faced within another topic and I made this topic separate because I wanted to focus on this specific problem, which would deviate from the other topic. However, if moderators feel otherwise then it will be fine if the topic is moved to the other topic. So the problem(which I still haven't solved) is dealing with finding an equation to predict the amount of matrix solutions for a given Collatz-Matrix equation, which is defined by as the following: [math]C(x)_{k\times d}\begin{Bmatrix} a_{f} &b_{f} \\ u_{f}&v_{f} \end{Bmatrix},s(k_{p},d_{p})[/math] Now, how these work is there could be multiple or just 1 matrix solution for a given Collatz-Matrix equation. For each matrix solution, the initial element lies in the coordinate given in s(). Then, the next element's placement is determine by which function(within the brackets) is used. If a_f is used, the element is placed above(if it can be done) the element at hand. If it is b_f, it goes to the left. If it is u_f, then it goes below, and if it is v_f it goes to the right. The next element's value will be based off the function used. Also, in this case every element must end up being a whole number. Since there are multiple ways to do this, there can be multiple matrix solutions. Now, here is some more information. Though I am assuming the weak version of the solution will also apply to the strong version as well. The weak version assumes there to be a ratio [math]\frac{d_{e}}{d_{i}}[/math] to exist within each function, where the Collatz-Matrix equation is set up as the following: [math]C(x)_{k\times d}\begin{Bmatrix} \frac{x}{r}&\frac{x-d_{e}}{d_{i}} \\ d_{i}x+d_{e}&rx \end{Bmatrix},s(k_{p},d_{p})[/math] The variable r is equal to [math]\frac{d_{i}\times\frac{\frac{\mathrm{d} }{\mathrm{d} x}\left ( u_{f}b_{f} \right )}{d_{e}}}{(1+d_{i}x)}[/math] If you need more information to solve this, please let me know. I will also continue to work on this problem.

I see your points. Time to scrap this idea. EDIT: Alleged wasn't a descriptor of me saying it isn't an axiom, but stating that there may be some lower system to prove the axiom that we don't know of(speculatively). However, this is already proven false.

I refer to the common IQ test(I think IQ?) where the task is to name as many things that a paper clip can be and do. So then the function would only be generalized with limitation. Let us assume that B is a theory which contains an axiom A and we are trying to prove A using B. This is where this is contradictory because you are trying to prove something that is unprovable and therefore you assume an axiom to be a theorem within B. However, we assume that A will always be an axiom rather than a theorem because we would also assume that there is no simpler rule under alleged axiom A. Therefore, wouldn't that have to be taken into consideration? You mean provide examples of tasks to complete with those tools?

You didn't say the patient had to be alive. But, all jokes aside, I my point is all of this is merely hypothetical. Same applies to the paper clip idea when finding what can be done with a paper clip. I think there would have to be some set of circumstances the idea would have to apply to this. EDIT: Had to fix some grammatical errors.

I looked up the surgery process, and one way it can be done with a hammer and anvil is using the anvil to break open the upper part of the skull and then use the sharp end of the hammer cut open the tissue that remains above the brain. Then, using the hammer, complete the surgery needed to be done. Remember, those solutions assume a set of particular axioms.

It is a hypothetical. You theoretically COULD, but the likelihood of succeeding with such tools would be 1/10^n. EDIT: In someways, I think this may be related to the P vs. NP problem because that problem is dealing with the question of whether a problem that currently lies in the NP spectrum of complexity can also exist in the P part of the spectrum. One speculative idea that could be presented is the idea of the reflective property of distribution dealing with algorithms. An algorithm that lies in the complex part of the spectrum also lies in the reflective side of the simplicity spectrum. Though, this is merely speculative.

I was thinking about the quote "Nothing is impossible" and it brought up the idea of carrying out a specific task the same, but with a different set of restrictions or rules applied to that task needed to be done. Yes, certain things are impossible because of the rules of physics and the rules of mathematics, but some how we find a way to accomplish that task another way. I find it interesting how this can be done even within a different set of rules and restrictions. So, it got me thinking that these tasks being done in a different set of restrictions can be generalized by a function that if you have found the process of completing a task within one set of restrictions then you can find the process of completing a task with any set of restrictions. What does anyone think about this idea? Is it something to think about? I put this in the mathematics section because it is taking an algorithm and defining it for all set of rules.

The main difference between the two is their use of different axioms, or assumed rules. For example, Euclidian geometry has the use of rules of parallel lines(Euclid's fifth postulate). Non Euclidian geometry consists of lines that curve towards or away from each other. http://en.m.wikipedia.org/wiki/Non-Euclidean_geometry

I was on tablet and didn't see those response. My apologies. Also, I want to make sure you knew that I didn't thumb you down.

Enlighten me oh wise one.