Zero

Zero indicates the absence of a quantity or a magnitude. It is so deeply rooted in our psyche today that nobody will possibly ask "What is zero?" From the beginning of the very creation of life, the feeling of lack of something or the vision of emptiness/void has been embedded by the creator in all living beings. While recognizing different things as well as the absence of one of these things are easy, it is not so easy to fathom the complete nothingness viz. the universal void. Although we have a very good understanding of nothingness or, equivalently, a zero today, our forefathers had devoted countless hours and arrived at the representation and integration of zero and its compatibility not only with all non-zero numbers but also with all conceivable environments only after many painstaking centuries. Zero can be viewed/perceived in two distinct forms: (i) as a number in our mundane affairs and (ii) as the horrific void or Absolute Reality in the spiritual plane/the ultimate state of mind.

Presented are the reasons why zero is a landmark discovery and why it has the potential to conjure up in an intense thinker the dreadful nothingness unlike those of other numbers such as 1, 2, and 3. Described are the representation of zero and its history including its deeper understanding via calculus, its occurrences and various roles in different countries as well as in sciences/engineering along with a stress on the Indian zero that is accepted as the time-invariant unique absolute zero. This is followed by the significant distinction between mathematics and computational mathematics and the concerned differences between the unique absolute zero and non-unique relative numerical zeros and their impact and importance in computations on a digital computer.

• Introduces the history of the value of zero and why it was a landmark discovery
• Discusses how zero is used in science and engineering and its use in different countries
• Explains how zero affects different mathematics and calculus

Students, researchers, and professors/teachers in any mathematical and computational sciences area such as Mathematics, Physics, Mathematical and Statistical Physics

Preface
Contents
1. Introduction
1.1 Matter versus non-matter
1.2 Zero in universal nothingness
1.3 Birth and five properties of zero
1.4 Zero is the very life of all sciences and engineering
1.5 Nomenclature and symbol of zero
1.6 Division by exact zero and non-exact zero

2. Why Zero is a Landmark Discovery and the Dreadful Void!
2.1 Zero and wheel: Greatest innovations
2.2 A landmark discovery
2.3 The dreadful void!
2.4 The Ultimate mind

3. Representation, History, Understanding, and Uses
3.1 Representation of nothingness — an important need toward progress
3.2 History
3.2.1 Prelude
3.2.2 Zero as a number used by Indians
3.2.3 Brahmagupta’s rules to compute with zero and later activities
3.2.4 Zero as a placeholder
3.2.5 Arithmetic operations using zero
3.2.6 7000-2000 BC: Decimal number system innovated that is universally used today
3.2.7 2000 BC-1000 AD: Zero fully developed with representation and arithmetic
3.2.8 1000-1900 AD: Introduction of Hindu-Arabic numeral system in Europe
3.2.9 1900-2015 AD: Impact on zero due to modern digital computer

4. Classical, Numerical, and Natural Mathematics with Calculus
4.1 Mathematics versus computational mathematics (numerical) with role of zero
4.2 Inputs and outputs make a vital difference
4.3 Floating-point representation of numbers and arithmetic
4.4 Dwarf and machine epsilon
4.5 The true zero and a local/numerical  zero 
4.6 Calculus: ultimate step in understanding mathematical zero since 3rd millennium BC
5. Zero in Sciences and Engineering, Its Use in Different Countries 
5.1 Physics/engineering
5.2 Chemistry
5.3 Computer science
5.4 Computational science/mathematics 
5.5 Algebra
5.6 Set theory
5.7 Propositional logic
5.8 Abstract algebra
5.9 Lattice theory
5.10 Recursion theory
5.11 Some branches of mathematics
5.12 Telephony
5.13 DVD
5.14 Roulette wheels
5.15 Tolerance
            5.16 Uses of zero in different countries with stress on Indian Zero and its transmission
         5.16.1 Babylon
         5.16.2 Greece
         5.16.3 India
         5.16.4 Sanskrit and English words for zero and infinity
         5.16.5 Significance of void and zero
         5.16.6 Central America
         5.16.7 Transmission of Indian mathematics to the west and to the east
5.16.8 Zero still had to pass through significant opposition

6. Conclusions
6.1 Concept of zero existed before Christian era
6.2 Existence of year zero in astronomical counting is advantageous and preserves compatibility with significance of AD, BC, CE, and BCE
6.3 Zero as a place-holder in Long Count dates
6.4 Representation of any information: Minimum two symbols are required ─ zero is one of them 
6.5 Influence by Vedic-Hindu-Buddhist legacy 
6.6 Why base 10 number system survives and used by one and all 
6.7 Universally accepted zero is the zero viewed and used by Indians
6.8 Psychological aspects of zero is distinct from those of non-zero numbers
6.9 Computational zero versus absolute zero and error
6.10 Zero in natural mathematics, mathematics, and computational mathematics
6.11 Is error in error-free computation zero? 
6.12 Is there anything beyond fundamental particle considered as a building block of matter?
6.13 Epoch: origin of an era
6.14 Revelation through intense concentration
6.15 Arabic inheritance of science from non-Arabic world and her contributions
6.16 Exact zero is usually unknown in physics
6.17 Quantum, relativistic, and absolute zeros in physics are not exact zeros
6.18 Zero or dot symbolizing beauty and eye of knowledge in Indian poetry and culture
6.19 Indian mathematicians and some Sanskrit terms concerning zero and place-value system
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6.20 Insightful comments and special terms related to zero/infinity
6.20.1 C. Seife, A.N. Whitehead, T. Danzig, and Lucretius
           6.20.2 The calculus and the Rig Veda
6.20.3 Zero for blast.
6.20.4 Ground zero and Zero hour
6.20.5 Counting from zero? John Conway and Richard Guy.
6.20.6 Archimedes
6.20.7 Holy Koran.
6.21 Root of the word zero
6.22 Zero and infinity in mathematics, physics, and beyond 
6.23 Zero space
6.24 The quantum universe: a zero-point fluctuation?
6.25 Dark matter: still in the dark in our quest for the origin of the universe
6.26 Concept of zero and non-zero in western and Indian cultures
6.27 Ramanujan and zero with its eternal spiritual significance
6.28 Why did the original name of zero come to be used for the whole set of Indo–Arabic numerals?  
6.29 Documents showing use of the place–value system and zero  
6.30 Ananta and Bindu in Hinduism
6.31 Working without concept of zero: Deterrent for Babylonians
References