Universal Numbers - The Universe Of Eternity “Every elementary number is respective with certain reference or standards and there exists no absolute elementary number that forms a basic building block of all numbers. Any set of elementary entities can be always broken down into smaller elementary entities, but this is all with the certain perspectives like ”urge to, keep on finding deep or more”. However, with the balanced perspective, its duality, which is zero and one in our mathematics. And same is followed by the universe too” Balram A. Shah Abstract The urge to understand the universe and solve some existing problems has led us to discover a special set of numbers that isn’t just a higher set of real and complex numbers but also handles zero and infinity in its true existence. This number system articulates a wide and very basic understanding of mathematics in its 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, frameworks, 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 some 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). 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. 1 of 49 2 of 49 1. Introduction The existence of any natural quantity in the universe are in the form of non-terminating decimal digits rather than terminating numbers but for various reasons, most of the time non-terminating numbers are used in the form of terminating numbers at the closest approximation. The human has no necessity to know every quantity in its full accurate manner in daily life rather to be in approximation. Generally, the sun doesn’t spend the same amount of time every single day nor two apples weighing the same have the same number of atoms. And if two atoms are of the same weight, it is expected both may not have the same number of subatomic particles in it. It's just a matter of fact that at what precision a person is dealing with numbers. On other hand, real numbers or complex are not enough to express these non-terminating numbers as this is not enough. When we say, this is one mango, we also know that mango is made up of many atomic particles and every mango has different numbers of atoms. So, saying one mango is generally correct but according to universe number is incorrect as, if we bring another single mango, it will not have same numbers of atomic particles. Similarly, it is very expected that the two same atoms will not have same number of building blocks entities that makes atom. We live in certain range of precision in this universe and we calculate the scale only in and around that range of precision but universe precision is not limited. The way, a recurring non-termination rational number cannot be described in a single sequence but requires a fraction which is a combination of numbers and arithmetic operator to describe its true existence, similarly, there exists an entirely new number system that requires a combination of numbers, arithmetic operators and the concept of infinity. Universal number maps to a specific real number but the number can change its virtue relatively to another number or type of mathematical operation it is involved in if those numbers are expressed in real number. Let us consider ab= but depending on some condition, ab and vice versa. For example, 0.99= 1 but that same 0.99 act as a different number in different conditions and it happens relatively to another number’s effect and type of operation it is involved in. There also exist certain conditions that a smaller number can suppress the existence of a larger number including infinitely larger number. 2. Universal Theory Theorem 1: There always exists a home for everything including the home itself. Irrespective of what basic system, framework, idea and things we are trying to create or assume, it always has a home in which it exists. Even a basic home(system) has its home. But we will never know all the aspects, property and nature of a home unless the home has the same property as the system in an infinite reparative process (infinite loop) or finite cyclic system (cyclic loop). Theorem 2: In the mathematical perspective, every change always remains balanced in the universe with reference to the neutral point. And if not, then some quantity has been ignored. Universal Numbers 3 of 49 Theorem 3: Any change gives rise to counter change and this counter change holds the potential to neutralize the self system or this counter change also holds the potential to create some changes in another surrounding system. However, someone may view this changes as positive aspects or anegative aspects based on consideration of reference point. It is just a matter of perspective. Knowingly or unknowingly, its viewers wish or mindset to see certain things in certain ways. Theorem 4: If any number is yielding multiple unique solutions then that number is the combination of multiple unique numbers. Everything system In the single dimensional universe, the only concept that exists is the endless number line made of an infinite number of points where it is inappropriate to assume any blank space rather there are only points everywhere on the number line. And any point on the number line is identical to any other point without any difference in any property and prospective among the points. Similarly, in three- dimensional, the entire space is made of points where the three-dimensional horizon is endless and the concept of center point does not it exist in any particular. Nothing system From the perspective of nothingness, there exist nothing, it simply means there is nothing to imagine. But this nothing is also part of the home if you know anything about it, including the void. Theorem 5: Nothing is nothing only in a particular system. But that nothing always resembles something if we consider that nothing from its home system or the higher home of the system. Nothing is something that makes no difference nor it resembles anything nor it makes sense in that system, but that nothing always resembles something from its home system or the higher home of the system. Example: Subadd system is the home for Muldive where unit one is nothing in Muldive system (real numbers) but one represents something in Subadd system (real numbers). Neutral State or a Triple state system. This can be imagined in the Subadd system as, there is a number zero that resembles nothing in the system and every time there arises any number, the system creates a counter number simultaneously in that system keeping the system as zero in the same moment. In other words, the system creates a number and counter number at the same moment keeping the entire system zero or balanced. So, the entire system as a whole is nothing and in a balanced state and represents the whole system. 3. Principle Theory of Universal number One of the ways, universal numbers can be understood as the consideration of the rate at which the Universal Numbers 4 of 49 real number was formed to its final precise value that is denoted in concise and precise value. These numbers are dynamic, it has infinite precision and cannot be represented without infinity or zero. The precise value of universal numbers remains unknown but its accuracy converges toward a specific real number and it tends to possess some properties and behaviors of that specific number. In this number system there exist three major points that are neutral point and two free ends which never ends. So, if there exists any number on this number line, there exists a counter number (inverse number) on the same number line except for a neutral number. This neutral point is different with respect to different frameworks of numbers and two simple frameworks are addition-subtraction (Subadd) and multiplication-division (Muldive). Definition [1]: In various number systems, all numbers are balanced from a specific reference point that does not have its own inverse or it acts as its own inverse and also its presence creates no effect or meaning in that number system. These numbers are termed as a neutral number of that system. Universal numbers system is established with the help of two major number frameworks that exist in day to day mathematics with common attributes.