Research Articles

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Next Generation Mathematics – The Universal Numbers (v5)

Abstract
The universal numbers (U) is a newly discovered number system where CϵU making it the largest number domain in mathematics. This system adds 0 and ∞ stably in the number line allowing us to conduct any operation with correct unique solutions and indeterminate forms are just a myth for this system. The difference between a universal number system and a complex number system are the rules for zero and infinity. The complex numbers make the mathematical operation simpler at the cost of locking the biggest domain of mathematics whereas Read More the rules of the universal number system revise some special rules given to zero and infinity automatically making mathematical operation a little bit heavier but with the advantages of opening a new biggest domain. A domain that unlocks the new and bizarre facts of mathematics and this universe.
The mathematical applications found in this system are extensively useful as this system simply eradicates the existence of indeterminate forms. This also opens a new and more clearer perspective of transcendental numbers giving a lot more understanding of π and e with new, simpler, and clear mathematical equations including a simple algebraic formula for negative factorial which is only possible in universal numbers. The behaviors of this system also shows that law of conservation of energy and basic properties of quantum physics are purely inherited mathematical properties that exist in all equation levels and it not a physical level phenomenon. Various other miscellaneous applications are also found such as, this domain gives a justified solution for 1-1+1-1+1…=1/2 which is difficult to be justified in complex numbers.
As this is a new domain, the research has infinite possibilities with infinite unique applications however this article structures the fundamentals and rules to dive in and operate in the universal number system seamlessly and stably to take the benefit of what universal number has to offer. Read Less

Keywords

Multidimensional number system, New number system, Highest domain range number system, Algebraic equation of negative factorials, Division by zero, 2=1, pi, e, Transcendental numbers, New division rule, Indeterminate forms solved, Zero, Infinity, Infinite series, Gamma function, Imaginary numbers, Conservation of energy mathematical proof.

Next Generation Mathematics: The Universal Number System (V3)
Abstract
The universal number system is newly discovered largest and extended number system that includes a complex number system within it and also increases logical and numerical accuracy exponentially. The way imaginary numbers are not required unless we deal with negative roots and want to standardize the process. Similarly, this system is only necessary if we want to deal with zeroes or infinities. As such unit’s definitions have been mathematically standardized along with a standardizing operational approach that gives the precise balanced output Read More for any mathematical operations with zeros and infinities.
Surprisingly, while dealing with standardized zero and infinity, some more hidden dimensions, domain and mathematical logical statements are discovered that increase the direct applications of mathematics beyond mathematics. With this domain addon, the system is able to express all the major properties of quantum physics & quantum computing, able to prove the conservation of energy mathematically, and a few more natural and scientific phenomena without creating any new definitions or including any physical quantities. And so, indicating such logical properties behind such physical phenomena in the universe are inherited properties of the mathematics.
So, in this article, its fundamentals, basic principles, and rules are established to support the smooth and balanced operation of the universal number system. Also, many application problems are solved in a standardized operational approach that may not be possible or may take very long R&D in real or complex number systems to get such results. Such as logical explanation for 1-1+1-1+1…=1/2, general solution for all indeterminate forms including any division by zero, newly discovered working formula for negative factorials, and direct connection of imaginary numbers with real number plain. Also, it enhances the understanding of zero, unity, infinity, i, π, e, x! and many more expressed in the result section indicating the consideration of this extended domain beneficial and fruitful in mathematics.
And, within this new domain, there are lot more pending unexplored discoveries as discussed in the “future research” section that may turn even more astonishing and fruitful in mathematics. Read Less

Keywords

Highly precise number system, Multidimensional number system, Newly discovered number system, Highest domain range number system, Negative factorials, Algebraic equation of negative factorials, Division by zero, New precise subtraction rule, New precise division rule, New precise exponential rule, Solved indeterminate forms, Zero, Infinity, Infinite series, Increased domain range, Universe oriented number system, Imaginary numbers, Negative number roots without using imaginary numbers, Quantum physics, Quantum computing, Alive numbers, Conservation of energy proof, Space and brick theory.

Next Generation Mathematics: The Universal Number System

Abstract
The Universal number system is a newly discovered vast number system with the domain that includes integers, real numbers, and complex numbers in its ecosystem. Also, magnitudes in this ecosystem are precisely controlled for every magnitude including the entire domain of &nbsp Read More complex numbers contains, and also other magnitudes such as zero, less than zero, infinity, and higher than infinity. Having precise control over such numbers allows us to conduct any operation with these magnitudes such as division by zero or multiplication by infinity, to handle function points precisely that are beyond infinity or below zero and many. This infinitely increased domain range beyond complex numbers helps us in understanding many real life phenomena, science, nature, and the unaversive very accurately in terms of depth and wideness. A few bizarre and interesting things noticed in this system are magnitudes are relative and they change their dimensions in certain circumstances. And this is why indeterminate forms including division by zero have no possible solution by just remaining in the real or complex number system which in turn represents just one dimension.
Using this infinitely high accuracy system, we also understand we are not just approximating the numbers in mathematics but it is found that unknowingly the outcome of equations and formulas are also been approximated for ease or reducing the complexity of the solution. And this leads in yielding a wrong solution in various corners of mathematics. Example: Multiplication of any magnitude by zero is zero which is a correct solution but it is an incorrect solution if we consider a certain level of precision. So, using this system, we can effectively use the approximated solution and handle it without getting into any invalid solution. Also, this system provides the ecosystem to conduct its required operation precisely and without any approximation, which the current system does not provide due to its limitation in the domain range.
So, in this article, its fundamentals, basic principles, and rules are established to support the smooth and balanced operation in the universal number system. Also, some application problems are solved that are generally not possible in the real or complex number system. However, the research on this topic is limited as it’s a fresh new discovery, and looking at the current potential, it can be well and easily predicted that a very bizarre understanding and extensive amount of applications are yet to come.
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Keywords

Higher Number system, Highly Precise Number System, Multidimension Number system, Newly Discovered Number System, Highest domain range number system, Negative Factorial, Division by Zero, Precise derived Algebraic equation, new precise subtraction rule, new precise division rule, new precise exponential rule, Solved Indeterminate Forms, Zero, Infinity, Infinite Series, Increased Domain Range, Real universe oriented number system, BBUM, Approximation of Equation.

Universal Numbers – The Universe Of Eternity

Abstract
The urge to understand the universe led us to a special set of numbers which isn’t just a higher set of real and complex numbers but it also handles zero and infinity in its true existence. This number system articulates a wide and very basic understanding of mathematics in its Read More natural form with respect to the universe. In real numbers, dividing by zero results in multiple solutions so it is best practice to avoid dividing by zero, but what if dividing by zero has a unique solution? Universal numbers carry additional accuracy about every number and produces unique results for every indeterminate form. Related to this number system, theories, framework, axioms, theorems and formulas are established. Also, some problems are solved which had no confirmed solutions in the past. Problems solved in this article gives more understanding about the imaginary number, calculus, infinite summation series, negative factorial, Euler’s number e, and mathematical constant π from a very new perspective. With these numbers, we also understand that zero, one, and mathematical constant e are standard reference points playing a very important role in mathematics. Universal number system simply opens a new horizon for entire mathematics and its property to holds additional details allows us to deal with every number precisely but may require computation intelligence and power for evaluation in many cases. The three major aspects of the universal number are the endless horizon of number scale, infinite precision of every number and the reference point (zero, one, e and π). Read Less

Keywords

Zero is one minus one, Complex numbers subset of universal numbers, division by zero, division by infinity, new and universal concept of zero and infinity, theory of universal numbers, negative factorial, alternative of infinitesimals, alternative of calculus, indeterminate form, equation of zero, alternative form of zero, Subadd framework, Muldive framework, indexing scale, indexing scale, universal forms and universal numbers.

The complete framework of Universal Numbers

Abstract
This paper contains the complete framework of universal numbers along with the universal forms with a complete framework. There are many limitations in real numbers over universal numbers that are discussed in this article. But equations related to the complete framework Read More of advanced number is rarely used in existing mathematics. So, very little research is conducted and research is been postponed for the future which can be conducted by anyone. Read Less

Keywords

Real numbers and complex numbers subset of advance numbers, division by zero, division by infinity, new and advanced framework of zero, equation of zero, alternative form of zero.

Equation invention model and a new built function with numerous interesting properties

Abstract
This research articulates an approach to invent a substantial equation even without having precise knowledge and skills in mathematics. A model is built such that software will take basic level information and give a complex level equation along with other outputs which make Read More the output equations easier to interpret, visualize and understand its correlations. This expands and amplifies once ability to invent potential equations. Using the model, new eight functions are built and are abbreviated as Couple-Quad Mirror Effect functions (C-Qme function). It is found that \({(a + {x^b})^{a – x{\,^b}}}\) is reflex of \({(a – {x^b})^{a + {x^{\,b}}}}\) about the y-axis line for the odd integer value of b. When all eight functions are plotted, any equation always intersects with the other two equation’s plot at different points for different values of a and b but the intersection angle always remain at ±45 degree from x–axis. Integration method refers that, the area under the curve \({(a + x)^{a – x}}\) and \({(a – x)^{a + x}}\) are equivalent. The slop of this equation lies one the Euler’s number “e” when \(x = 0\) and on \({e^{ – 1}}\) when \(a = 0.\) Paatu function is only one or one of the rarest curves where the same 2-D geometric curve is represented by 8 different functions with only difference in its arithmetic operators of the functions. Also, this is one of the simplest equations to form a beautiful heart geometry. Read Less

Keywords

New functions Inventions, mathematical approach, equation computation, multiple equations with equivalent area, Algebra and calculus analysis, different intersection point with same intersection angle, C-Qme Function, Paatu Equation, heart equation.

Special equation from Binomial transform and nth order finite difference

Abstract
Using numerical analysis and tables, nth order backward difference of exponential function is obtained. Further analyzing the obtained equation yields a special identity given as Read More \[\sum\limits_{k\, = \,0}^n {{{( – 1)}^k}\,\frac{{{{(x – \,k)}^{n\,\, – m}}}}{{(n\, – \,k – m)!\,k!}}\,} \, = \,\,\sum\limits_{k\, = \,0}^{n\, – m} {{{( – 1)}^k}\,\frac{{{{(x – \,k)}^{n\, – m}}}}{{(n\, – \,k – m)!\,k!}}\,} = \,\,1\,\,\,:\,\,\left\{ {\begin{array}{*{20}{c}}
{x \in R}\\
{n \in \,W}\\
{m\, \in \,W\,\,{\rm{:}}\,\,m \le \,n}
\end{array}} \right.\]
This equation yields the value of negative integer factorial, zero factorial and zero to the power zero which is currently indeterminate forms along with other unknown values. With this equation, we also conclude the product of zero and infinity is unity within certain parameters. Read Less

Keywords

Negative factorial equal to plus-minus infinity, power factorial table, nth order backward difference, zero to the power zero is one, special sequence series in binomial transform, new series equation.