Exponents' Alternative Dark Forms And Surpassing Limitations Set By Abel-Ruffini's Theorem

This list of mathematical arrangement are hidden ways to solve mathematical problems. I will attempt to dismantle Abel-Ruffini's theorem with some tools targeting quantitative and proportional operations. I re-established some axioms for this puzzle and will attempt to solve every degree of polynomial equation up to the dreaded quintic. I thought that most of these examples required little clarity. Aside from +- b values, only from example (6) onward did I utilize quantitative approaches in addition to proportion techniques shown from the start. For the power rule in example (8), I found that exponents could be used as both a percentile amplification and as a quantitative denominator. I didn't bother to use the power rule's derivatives. I'll admit that there might be better ways to rearrange exponents and their bases.  Example (9), on the execution form, was evidence for the duplication of values. 16 became 48 in total. By recognizing these duplicates, one could infer systematic changes to find multiple substitutive values akin to basic algebra. These approaches allowed an analyst to realize that numeric constructs were indeed ordinary symbols like letter constructs A, B, C, and D. Mental logic and real references were, and are,  separate from numerical limitations. 16 could easily be replaced with F in my purely formulaic form. What's unique to numbers were their quantitative and proportional realizations which were further manipulated.  These mathematical models were limited to linearly segregated dimensions. This meant that they had no accurate 2D or higher dimensional approaches; they are relegated to imaginary line elements. Since there was , and is,  a real world outside of  one's Linear Legacy Mathematical Flat Earth Mental Paradigms, it was easy to use the aesthetes of art to physically draw higher dimensional models when one had already settled there by default.  The human's current conscious cognitive capacity did not reflect higher dimensionalities which were intuitive of its reality and sub-conscious to unconscious mental dashboard. The human's utilization of value, quantity, percentage, orientation, quality, and other calculative attributes remained in its infancy with many malpractices as ill-references. 

Exponents of the second degree are completely solved. Therefore the classic quadratic equation will be solvable. X^2 perishes. Later, I will present my examples. It will be interesting if higher order exponents follow similar patterns. If confirmed, you can pretty much say good bye to Abel Ruffini's  impossible theorem. A new array of calculative techniques was born from Darkness. Note: Any errors will be corrected at a later time. 

On this blog, I dedicated a page to the recursion of time. In order to shuffle attributes belonging to power, I transformed its quadratic exponent to 1/2. By uncovering the value associated with a quadratic system's iteration of time, I'm allowed to quantify its additive recursion as a denominator in order to retrieve a powered outcome's square root or base. As far as I was concerned, this technique of mine applied to all quadratic power bases from a minimum of 1^2 to a maximum of #^2. Any power base could potentially be recovered as shown in my prior posts. I personally recommended whole numbers starting from 1 as shown by examples (10a_b)and Area Mitosis, but it seemed decimals had to exist as a demand by the time's iteration. Certainly, I don't necessitate a power rule, but once activated, one might as well use decimals and real numbers.  My examples don't require much explanation. Ideally, if one uses integers, positive and its opposing operator(negative) will adjust depending on the status for each variable in an expression. If one powered a decimal base, one must allocate those missing values for other variables in order to rebalance the equation via the change method. This method manipulates ill-references by creating duplicate values and variables. It's something that I personally don't recommend. I recommend percentile functions as a mapping for quantitative foundations with accurate and updated references.   

 By analyzing cubic polynomials, I witness the original pattern remain.  Determined to uncover hidden mechanics which might make my quadratic procedure more instructionally robust, I developed the pattern for cubic polynomials. The method was further refined offline and is now what you currently see. This angle revealed what was really going on with time. Time faced an exponential increase. I might increase the values in order to move away from fractional limits by setting a base of 1 or above for recursive time. I expect there to be a limit to how far into the decimal realm one might go while maintaining a constant output value for all X. That decimal floor should be proportional to the magnitude of the equation's maximal output. 

All previous principles apply to both quartic polynomial and quintic function. A summarization for solving all polynomials is present. Some problematic contradictions are negative and positive variations. I notice that I have to create these conflicting axioms to derive an answer. Is the answer accurate? Is the formula's structure accurate? (12) illustrates the factoring method which doesn't include a recursion of time.(12)'s -8x and -9x strikes me as odd because they mean the x is negative. So, it begs the question, does -x = +x ? The letter obscures the depth of the question, so I replace them with something more attune to calculative questions. Does -2 = +2 ? Even Google doesn't have an answer. Common conjecture might say that -1(2) = +1(2), therefore 2 = 2. Soooo... does -1 = +1 though? This question cannot be escaped. This is a result of not determining if negative has a size or not. It behaves as if it is equal and opposite to its positive counterpart while being categorically different number systems. - charge means greater quantities of electrons while positive denotes as less.  If  (+ = -) , negative numbers are redundant beyond neutralization. If not, it's a fundamental flaw in mathematics. Based on size and quantity, these shouldn't be entirely equivalent. Thus, these X aren't similar. Furthermore, before any operation +X * +X should attract like terms -X -X , but they don't. ( - * - )= + is another contradiction, since negatives increase. It also means compounding of smaller sizes yet negative gets smaller.  (+ * - )= - reveals distinctions based on condition. See , (+ * +) = +.  If negative is indeed a reflection of positive, why doesn't   (+ * -) = + ? In the end , mathematics is mere instructions. I'll keep this in mind going forward, but I will attempt to decode the rest. You never know what I might find because Flat-Earth Legacy Math's errors can help me develop better calculative instructions by not applying theirs. Very important, one shouldn't allow Phd Nobels to sidestep and gaslight you with Gödel's Incompleteness theorem. All versions can be summarized as follows:

In conclusion, what's essential to understand was that calculations didn't advance beyond prehistoric tribal means. DRC's Ishango Bone featured fundamental concepts like decimal, fractions, prime numbers with operations like addition , subtraction, division, and multiplication. What changed as knowledge of materials increased was the refinement of measurements beyond bones, sticks, and ropes. Other aspects like the simplicity of drawing  less cumbersome symbols ,instead of many more strokes, allowed for more sequence of operations within limits of space-time.  Linear algebra was already there since Ancient Kemet and The Indus Valley, and I could make the argument that it was there since the DRC. I+I, I-I, I*I, and I/I are no different than 1+1,1*1,1-1,1/1 or x*x, x+x , x-x, and x/x. The Babylonians, or ancient Iraqis, inscribed additional basic instructions as quadratic and cubic polynomials. They are not beyond linear measurements as shown. They cannot describe an accurate 2D structure. They can only pretend by drawing , which prehistoric tribes were designing geometric shapes without a fine-tuned knowledge of its measured dimensions since ages. Evidence for 3D manipulate existed as pyramids which can be found in many continents.  It should be clear that the only value in modern calculations were their unique sequence implementing these fundamentals, what they properly referenced, and their philosophies behind their instructions that command Nature to do its work in a determined and organized fashion. It's always mindless atomic particles doing work. Organism merely arranged them. I will continue to create and gather practical operations and knowledge from rational sources to devise an elevated model beyond these flat-earth bone models. 

... Soon, my greed for allocating metacognition and applying all wisdom and knowledge will transcend serpentine. I'll become a dragon!!!! Recursion and Division Flaws, Mathematical And Logical Incoherence , Ill-References

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