Peter kosc, LLC
Books by peter kosc
This first book of the series on the polarized number system claims that the basics of mathematics we have been taught for centuries are flawed because mathematicians got it all wrong regarding understanding positive, negative, and absolute-value numbers. Even some of the most elementary mathematical operations in the real number system cannot be solved using the currently accepted rules of mathematics. Therefore, we must resort to clever excuses in the form of exceptions to the rules whenever the rules do not make sense.
If you consider such an assessment laughable, absurd, or flatly insulting, please try to divide by zero or find the real square roots of the negative numbers. If you fail, it is not because the solutions are not defined or they do not exist, but instead because the real number system is obsolete. It does not have the proper tools to handle such elementary operations properly.
It is a monumental task to convince the mathematical community that “we got it all wrong” regarding the basics of mathematics. Therefore, the book contains numerous examples of elementary operations supported by logical reasoning. It is written as step-by-step instructions, a reference manual, or a textbook with exercises, and thus may be overly detailed, repetitious, tedious, or exhausting for many.
Suppose you want to read a clear, concise, and complete reprint of popular mathematical concepts in one sitting. Perhaps the book’s subject may not suit you in such a case because it introduces original number systems and mathematical concepts that go against well-established traditional mathematical principles. Instead, the book is for those willing to read some passages several times to gain an understanding. It is for those who are not afraid to reconsider their mathematical knowledge.
As introduced in the book, contrary to the traditional understanding, all numbers, including zero, can be positive or negative in the polarized number system; however, absolute value numbers are not positive. Positive and negative numbers in the polarized number system fundamentally differ from positive and negative numbers in the real number system. Therefore, mathematical operations in both number systems lead to conflicting results.
POLARIZED NUMBER SYSTEM - 2
An Alternative to the Dogmatic Real Number System
Available now on Amazon.
This second book in the polarized number system series continues to demonstrate the fundamental properties of positive and negative numbers. It intends to convince the reader and the mathematical establishment that positive and negative numbers are vectors, not scalars, as in modern mathematics. The traditional understanding is gravely flawed and obsolete; therefore, finding the real square roots of negative numbers is impossible in the real number system. On the contrary, the book shows that the task is a straightforward process in the polarized number system.
After a brief review of Volume 1, the book uses the positive and negative electric properties of protons and electrons to demonstrate basic mathematical operations such as multiplication, division, the square function, and the square root function. The subsequent section employs the positive and negative properties of cash and debt, respectively, for similar operations. Both sections present the concept of negative areas, laying the foundations for the Pythagorean theorem with positive and negative areas.
Like Volume 1, the book contains numerous detailed examples or exercises of basic mathematical operations. The overly detailed nature of the book is not because the subject is complicated. Instead, it is because the mathematical establishment firmly believes in their understanding and, perhaps, leaves no room for alternatives. Thus, any significant changes to the dogmatic mathematics basics would send shockwaves through centuries-old teaching.
POLARIZED NUMBER SYSTEM - 3
The Pythagorean Theorem for Positive and Negative Areas
Available now on Amazon.
The Pythagorean theorem is considered one of the greatest discoveries in mathematics and geometry. It states that the sum of the areas of squares constructed on two shorter sides of a right triangle is equal to the area of the square on the longest side.
Such an understanding has been known and unchanged for millennia. Believe it or not, such an interpretation of the relationship between the sides of the right triangle is flawed because the Pythagorean theorem works only for certain, not all, right triangles. Within the framework of the real number system, not the complex number system, the areas are always positive, with the largest square always being on the hypotenuse.
This book shows that contrary to modern mathematics, the Pythagorean theorem in its current form is only a variant of a much broader understanding within the polarized number system. The Pythagorean theorem in the polarized number system states that the sum of the areas of squares on two sides of a right triangle is equal to the area of the square on the third side. The significant difference between the two interpretations is that there is no restriction on which two sides are added. In addition, the areas of squares can be positive or negative.
The Polarized Number System series books demonstrate that the real number system, the basis for modern mathematics, is flawed or incomplete at best. It lacks an understanding of the fundamentals of mathematics. The understanding of positive and negative numbers is rather nonexistent. Thus, the Pythagorean theorem fails for right triangles with negative areas presented in this book.
POLARIZED NUMBER SYSTEM - 4
Positive, Negative, Surplus, Deficit, and Absolute Value in Number Systems with Mass
Available now on Amazon.
Suppose the task is to draw a typical real number line. In such a case, zero and two sets of numbers are needed to accomplish the task. Positive numbers are generally on the right side of zero, and negative numbers are on the left. Regardless of classification or notation, each number can be considered unique because no other numbers can share the exact location on the number line.
Despite being accepted by the mathematical establishment for centuries, such an understanding is flawed because it does not correspond to the true fundamental properties of real numbers.
This book demonstrates that real numbers in the polarized number system can be grouped into nine, not two, unique sets. Therefore, nine unique variants of every number exist on a number line in the polarized number system. Believe it or not, nine different ones can be explicitly depicted on such number lines without coinciding with any other numbers.
The goal of the book is to show that “positive,” “plus,” and less-commonly used “surplus” represent fundamentally different concepts and cannot be used interchangeably. Similarly, “negative,” “minus,” and less-commonly used “deficit” represent fundamentally different concepts and cannot be mistaken for one another. In addition, this book proposes a few variants of absolute value numbers that exist in the polarized number system. Readers will discover that absolute values can also be negative.
In addition, this book shows that mathematical operations with nine sets of numbers can be impractical. Therefore, such number systems or lines can be simplified. However, simplifying explicit mathematical concepts can be challenging because it can lead to contradicting results or paradoxes, as often happens in modern mathematics.