scholarly journals Advanced number system – The universe of all numbers where anything is possible

2020 ◽  
Author(s):  
Balram A Shah
Keyword(s):  
Multiple Solutions ◽  
Best Practice ◽  
Number System ◽  
Complex Numbers ◽  
Real Numbers ◽  
The Past ◽  
Indeterminate Form ◽  
The Universe ◽  
Imaginary Number ◽  
Mathematical Constant

This research introduces a new scope in mathematics with new numbers that already exist in everyday mathematics but very difficult to get noticed. These numbers are termed as advanced numbers where entire real numbers, including complex numbers are the subset of this number’s universe. Dividing by zero results in multiple solutions so it is the best practice to not divide by zero, but what if dividing by zero have a unique solution? These numbers carry additional details about every number that it produces unique results for every indeterminate form, it allows us to divide by zero and even allows us to deal with infinite values uniquely. So, related to this number, theories, framework, axioms, theorems and formulas are established and some problems are solved which had no confirmed solutions in the past. Problems solved in this article will help us to understand little more about imaginary number, calculus, infinite summation series, negative factorial, Euler’s number e and mathematical constant π in very new prospective. With these numbers, we also understand that zero and one are very sophisticated numbers than any numbers and can lead to form any number. Advance number system simply opens a new horizon for entire mathematics and holds so much detailed precision about every number that it may require computation intelligence and power in certain situations to evaluate it.

scholarly journals Complex roots of polynomials and their computation with the help of Scientific Calculators

BIBECHANA ◽  
2012 ◽  
Vol 9 ◽  
pp. 18-27
Author(s):  
Mohd Yusuf Yasin
Keyword(s):  
Number System ◽  
Complex Numbers ◽  
Real Numbers ◽  
Engineering Technology ◽  
The Real ◽  
Complex Roots ◽  
Wide Range ◽  
Range Of Functions ◽  
Imaginary Number

Real numbers are something which are associated with the practical life. This number system is one dimensional. Situations arise when the real numbers fail to provide a solution. Perhaps the Italian mathematician Gerolamo Cardano is the first known mathematician who pointed out the necessity of imaginary and complex numbers. Complex numbers are now a vital part of sciences and are used in various branches of engineering, technology, electromagnetism, quantum theory, chaos theory etc. A complex number constitutes a real number along with an imaginary number that lies on the quadrature axis and gives an additional dimension to the number system. Therefore any computation based on complex numbers, is usually complex because both the real and imaginary parts of the number are to be simultaneously dealt with. Modern scientific calculators are capable of performing on a wide range of functions on complex numbers in their COMP and CMPLX modes with an equal ease as with the real numbers. In this work, the use of scientific calculators (Casio brand) for efficient determination of complex roots of various types of equations is discussed. DOI: http://dx.doi.org/10.3126/bibechana.v9i0.7148 BIBECHANA 9 (2013) 18-27

Complex Modular Numbers: Complex Numbers Need not be Complex

1976 ◽  
Vol 69 (1) ◽  
pp. 53-54
Author(s):  
Susan J. Grant ◽  
Ward R. Stewart
Keyword(s):  
Real Number ◽  
Complex Number ◽  
Number System ◽  
Complex Numbers ◽  
Negative Number ◽  
Real Numbers ◽  
The Real ◽  
Equivalent Equation ◽  
Imaginary Number

Most students are faced with the task of solving the equation x2 + 1 = 0 over the real numbers at some time in their algebra classes. After they substitute values for x unsuccessfully, they usually attempt to solve the equivalent equation x2 = -1. They soon realize that it is impossible to square a real number and obtain a negative number. At this point their teacher may define the imaginary number i to be and then proceed to develop the complex number system.

i

2020 ◽  
pp. 93-103
Author(s):  
Marcel Danesi
Keyword(s):  
Quantum Theory ◽  
Electromagnetic Radiation ◽  
Quadratic Equation ◽  
Complex Numbers ◽  
Human History ◽  
Real Numbers ◽  
Electric Circuits ◽  
René Descartes ◽  
New Ideas ◽  
Imaginary Number

What kind of number is √−1? In a way that parallels the unexpected discovery of √2 by the Pythagoreans, when this number surfaced as a solution to a quadratic equation, mathematicians asked themselves what it could possibly mean. Not knowing what to call it, René Descartes named it an imaginary number. Like the irrationals, the discovery of i led to new ideas and discoveries. One of these was complex numbers—numbers having the form (a + bi), where a and b are real numbers and i is √−1. Incredibly, complex numbers turn out to have many applications. They are used to describe electric circuits and electromagnetic radiation and they are fundamental to quantum theory in physics. This chapter deals with imaginary numbers, which constitute another of the great ideas of mathematics that have not only changed the course of mathematics but also of human history.

Quaternions: The hypercomplex number system

2008 ◽  
Vol 92 (525) ◽  
pp. 431-436 ◽  
Author(s):  
Sandra Pulver
Keyword(s):  
Real Axis ◽  
Imaginary Axis ◽  
Vertical Axis ◽  
Number System ◽  
Real Coefficient ◽  
Complex Numbers ◽  
Square Root ◽  
Real Numbers ◽  
The Real ◽  
Hypercomplex Number

Are there solutions of the equation x2 + 1 = 0 ? Carl Fredrich Gauss (1777–1855) conjectured that there was a solution and that it was the square root of - 1 . But since the squares of all real numbers, positive or negative, are positive, Gauss introduced a fanciful idea. His solution to this equation was , which he named i. He integrated i with the real numbers to form a set known as , the complex numbers, where each element in that set was of the form a + bi, where a, . Gauss illustrated this on a graph, the horizontal axis became the real axis and represented the real coefficient, while the vertical axis became the imaginary axis and represented the imaginary coefficient.

scholarly journals Towards Formulation of a Complex Binary Number System

2002 ◽  
Vol 7 (1) ◽  
pp. 199
Author(s):  
Tariq Jamil ◽  
David Blest ◽  
Amer Al-Habsi
Keyword(s):  
Complex Number ◽  
Computer Arithmetic ◽  
Number System ◽  
Divide And Conquer ◽  
Complex Numbers ◽  
Binary Number ◽  
Computer Engineering ◽  
Real Numbers ◽  
Arithmetic Operations ◽  
The Individual

For years complex numbers have been treated as distant relatives of real numbers despite their widespread applications in the fields of electrical and computer engineering. These days computer operations involving complex numbers are most commonly performed by applying divide-and-conquer technique whereby each complex number is separated into its real and imaginary parts, operations are carried out on each group of real and imaginary components, and then the final result of the operation is obtained by accumulating the individual results of the real and imaginary components. This technique forsakes the advantages of using complex numbers in computer arithmetic and there exists a need, at least for some problems, to treat a complex number as one unit and to carry out all operations in this form. In this paper, we have analyzed and proposed a (–1–j)-base binary number system for complex numbers. We have discussed the arithmetic operations of two such binary numbers and outlined work which is currently underway in this area of computer arithmetic.  

scholarly journals Inequality in the Universe, Imaginary Numbers and a Brief Solution to P=NP? Problem

2019 ◽  
Author(s):  
Mesut Kavak
Keyword(s):  
Euclidean Geometry ◽  
Complex Numbers ◽  
Real Numbers ◽  
Riemann Geometry ◽  
Physical Phenomena ◽  
Actual Geometry ◽  
Np Problem ◽  
The Universe

While I was working about some basic physical phenomena, I discovered some geometric relations that also interest mathematics. In this work, I applied the rules I have been proven to P=NP? problem over impossibility of perpendicularity in the universe. It also brings out extremely interesting results out like imaginary numbers which are known as real numbers currently. Also it seems that Euclidean Geometry is impossible. The actual geometry is Riemann Geometry and complex numbers are real.

scholarly journals A New Set Theory for Analysis

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 31
Author(s):  
Juan Ramírez
Keyword(s):  
Real Number ◽  
Number System ◽  
Order Structure ◽  
Natural Numbers ◽  
Real Numbers ◽  
The Real ◽  
Power Set ◽  
Universe Of Sets ◽  
The Universe ◽  
Real Number System

We provide a canonical construction of the natural numbers in the universe of sets. Then, the power set of the natural numbers is given the structure of the real number system. For this, we prove the co-finite topology, C o f ( N ) , is isomorphic to the natural numbers. Then, we prove the power set of integers, 2 Z , contains a subset isomorphic to the non-negative real numbers, with all its defining structures of operations and order. We use these results to give the power set, 2 N , the structure of the real number system. We give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. Supremum and infimum functions are explicitly constructed, also. Section 6 contains the main results. We propose a new axiomatic basis for analysis, which represents real numbers as sets of natural numbers. We answer Benacerraf’s identification problem by giving a canonical representation of natural numbers, and then real numbers, in the universe of sets. In the last section, we provide a series of graphic representations and physical models of the real number system. We conclude that the system of real numbers is completely defined by the order structure of natural numbers and the operations in the universe of sets.

Math Roots: Ratios and Proportions: They Are Not All Greek to Me

2009 ◽  
Vol 14 (6) ◽  
pp. 370-378
Author(s):  
Joanne E. Snow ◽  
Mary K. Porter
Keyword(s):  
Number System ◽  
Rational Numbers ◽  
Real Numbers ◽  
Irrational Numbers ◽  
Line Segments ◽  
Whole Numbers ◽  
The Past ◽  
Geometric Objects ◽  
History Of

Today, the concept of number includes the sets of whole numbers, integers, rational numbers, and real numbers. This was not always so. At the time of Euclid (circa 330-270 BC), the only numbers used were whole numbers. To express quantitative relationships among geometric objects, such as line segments, triangles, circles, and spheres, the Greeks used ratios and proportions but not real numbers (fractions or irrational numbers). Although today we have full use of the number system, we still find ratios and proportions useful and effective when comparing quantities. In this article, we examine the history of ratios and proportions and their value to people from the past through the present.

Enlightening Symbols

2016 ◽  
Author(s):  
Joseph Mazur
Keyword(s):  
Sixteenth Century ◽  
Number System ◽  
Psychological Effects ◽  
Mathematical Notation ◽  
Rhetorical Style ◽  
The Past ◽  
Mathematical Symbols ◽  
Before And After ◽  
New Ideas ◽  
Different Cultures

While all of us regularly use basic mathematical symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? This book explains the fascinating history behind the development of our mathematical notation system. It shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, the book looks at how historians have disagreed over the origins of the number system for the past two centuries. It follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. It also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. It considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

Anxiety Disorders’ Effect on College and University Students’ Mental Health: A Common and Growing Concern

2020 ◽  
Vol 9 (2) ◽  
pp. 82-90
Author(s):  
Matthew J. Pesko
Keyword(s):  
Mental Health ◽  
Anxiety Disorders ◽  
University Students ◽  
Best Practice ◽  
Epidemiological Studies ◽  
Student Population ◽  
Adult Student ◽  
College And University ◽  
The Past ◽  
Mental Health Settings

Anxiety disorders are commonly experienced by college and university students and should be routinely assessed in mental health settings. Epidemiological studies suggest that the burden of these illnesses has greatly expanded even over the past decade. Factors that contribute to the experience of an anxiety disorder in a young adult student population are considered herein. The best practice for evaluation and treatment of these disorders is presented based on the review of available literature in this field. Special attention is paid to the concept of resilience as it pertains to anxiety disorders in the student population.

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