МЕДИЦИНА, ПЕДАГОГИКА И ТЕХНОЛОГИЯ:
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THE CONCEPT OF ZERO. (FROM THE PAST TO THE PRESENT)
Khudaikulova Saida Zakirovna
Teacher of Termez State Pedagogical Institute
Phone: +99890-246-47-47
Khalilova Romina Muslihiddinovna
2nd-year student of
Temez State Pedagogical Institute
Key words
: Zero, Indian Mathematics, Modern Technology, Probability Theory,
Philosophy.
Abstract
: This article discusses the emergence, development, and role of the concept
of "zero," which holds a significant place in the history of mathematics. It explores
fascinating facts related to the discovery of zero in India and the Islamic world, as well
as its introduction to Europe. Additionally, the philosophical and practical importance
of zero is examined.
One of the greatest discoveries in the history of mathematics is the concept of
“zero”. Today, this concept, which is an integral part of mathematical practice, initially
started as a simple symbol. However, its true power and potential were revealed later
with the advancement of human knowledge and science. This article explores the origin
of the concept of zero, its development over time, and its role in various fields of
science.
Zero (*nullus* in Latin, meaning "nothing"), or "nol," is the number that represents the
boundary between positive and negative numbers. Main properties:
The earliest ancestor of zero is considered a special symbol used to indicate an empty
place in the Babylonian numeral system, which was in use until the 5th century BCE.
Ancient Greek astronomers adopted the Babylonian base-60 numeral system but
replaced the cuneiform symbols with letters for denoting numbers. In their system, zero
was not considered a number. To mark the missing place in the base-60 system, they
used the first letter of the word
ouden
(meaning "nothing"), resembling the modern "0"
(Reference:
Young Mathematician's Encyclopedia
, Tashkent, Encyclopedia Editorial
Board, 1991, p. 273).
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The Origin of the Concept of Zero:
In early mathematical cultures, the concept of
"zero" did not exist. For example, the Roman numeral system lacked a symbol for "0."
However, as humanity's needs for calculations grew, the use of zero became essential.
Babylonian Culture (3000 BCE)
Babylonian mathematicians used a placeholder to signify the absence of a value
between numbers. However, this was not a fully developed concept of zero as we
understand it today.
Maya Civilization
By the 4th century CE, the Maya civilization had a clear use of zero in their calendar
systems. They used a distinct symbol to represent zero, making it one of the earliest
known instances of zero being used as a number in calculations.
Indian Mathematics
The true birth of the concept of "zero" occurred in India. In the 5th century,
mathematicians like Brahmagupta and Aryabhata introduced zero as a numeral and
developed a system for using it in calculations. Brahmagupta formulated the first rules
for operations involving zero, including multiplication and division, laying the
foundation for its mathematical application.
Development of Zero in the Islamic World
During the Middle Ages, the Islamic world became a center of flourishing mathematics
and science. Scholars in the Islamic world not only adopted the concept of zero but
also sought to understand it from both mathematical and philosophical perspectives.
They played a pivotal role in disseminating and further developing zero within the
decimal numeral system, integrating it into advanced calculations and scientific
endeavors.
Al-Khwarizmi
The famous mathematician Muhammad ibn Musa al-Khwarizmi introduced Indian
numerals (including zero) to the Arab world. Through his works, Europe came to
understand the concept of zero. The term "algebra" itself originates from al-
Khwarizmi’s book
Al-Jabr
. Al-Khwarizmi detailed the arithmetic operations
(algorithms) based on the Hindu system, and he placed great emphasis on the concept
of "circle" to represent zero in the process of addition and subtraction. He wrote: "If
you want to add a number to another or subtract one number from another, arrange
both numbers in two rows—one below the other—aligning the ones place under the
ones place, the tens place under the tens place, and so on. If you want to add two
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numbers, for example, add each place value to its corresponding place value above it,
i.e., add the ones to the ones, and the tens to the tens. If at any place, such as the ones
or tens, or any other place, the sum reaches ten, replace it with one and carry it over to
the next place. For example, if you have ten ones in the ones place, make it one and
carry it to the tens place, where it will represent ten. If anything smaller than ten
remains in a place or if the number itself is smaller than ten, leave it in its place. If
nothing remains, place a circle to avoid leaving a place empty. But the circle must
remain there, as if it is left empty, the places will diminish and the second position will
mistakenly be considered the first, leading to an error in your calculation.”
(
Muhammad ibn Musa al-Khwarizmi. Selected Works
. Tashkent, "Fan", 1983, pp. 63-
64).
The Introduction of Zero to Europe
The concept of zero faced significant resistance in Europe for a long time. The shift
from the Roman numeral system to one that accepted zero took time. In the 13th
century, Leonardo Fibonacci introduced the concept of zero and the Hindu-Arabic
numeral system to the European scholarly world in his book *Liber Abaci*. Ultimately,
zero became the foundation of the modern decimal system and was widely adopted
worldwide. During the Middle Ages, the Church opposed the use of zero, as it was
associated with the idea of "emptiness" or "nothingness," which conflicted with
religious beliefs.
The contribution of the Italian mathematician Leonardo Fibonacci (1170–1240) to
the teaching of arithmetic introduced in Western countries is significant. He traveled
to the East and studied the achievements of arithmetic and algebra from the works of
Indian scholars and Muhammad Musa al-Khwarizmi, playing a major role in their
widespread adoption in the West. His 1202 work,
The Book of the Abacus
, served as
an excellent resource on arithmetic and algebra based on the decimal numeral system.
The scholar expressed the Arabic word
as-sifr
as
zephirum
(from the Latin
zephyrus
,
meaning "zephyr" or "west wind").
Zero was expressed in Latin with the word
nullius
(meaning "none"). In translations
into many other languages, the term
sifr
became
sifra
and was widely used for a long
time.
When Arabic treatises were translated into Latin in the 12th century, the symbol for
zero ("0") was referred to as
circulus
(little circle) or
nulla figura
(no figure)
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(Matvievskaya G.,
The Development of the Doctrine of Numbers in Europe until the
17th Century
, Tashkent, "Fan", 1971, p. 72).
The use of zero as a number in mathematical operations was approached differently
by scholars both before and after al-Khwarizmi. Jordanus de Nemore (13th century), a
promoter of Indian and Arabic numerals in Europe, used zero in the form of
sifra
. In
the works of Chuquet (15th century), zero was referred to as
nulla
and
chiffre
,
influencing the terminology in France (
chiffre
) and in Italy, where
zephirum
evolved
into
zero
. Similarly, the term
libra
("pound") gave rise to
lira
. Later, the use of the
form
zero
became standardized in France to denote zero.
Pacioli (15th century) recognized zero as a number, while the Dutch mathematician
Girard (who died in 1632) acknowledged it both as a number and as the root of
equations. Vallis, however, argued that "zero is not a number" (Depman I.,
History of
Arithmetic
, Moscow, "Prosveshchenie", 1963, pp. 110–111).
The role of zero in modern science and technology.
Today, zero is fundamental in
mathematical analysis, algebra, probability theory, and various technological
advancements. It serves as the cornerstone of the binary system, which underpins
computer science and digital technology. Zero is essential in defining limits, solving
equations, modeling probabilities, and representing null states in data systems,
highlighting its indispensable contribution to contemporary science and innovation.
Computer Technology:
The concepts of zero and one (0 and 1) form the foundation
of the binary system, which is the basis for the operation of all computers, smartphones,
and programming languages. This binary system enables data storage, processing, and
communication, making it the core of modern digital technology.
Physics and Cosmology:
Zero plays a crucial role in concepts such as zero energy and
vacuum. For instance, the concept of "absolute zero" is fundamental in
thermodynamics, representing the theoretical temperature at which all molecular
motion ceases. In cosmology, the idea of a vacuum, defined as a region with zero matter
or energy density, is essential for understanding the nature of space-time and the
universe's evolution.
The Philosophical Meaning of Zero:
Zero is not merely a number but also a profound
philosophical concept. It symbolizes "emptiness," "nothingness," and the boundaries
of existence. In Eastern philosophy, the ideas of nothingness and emptiness represent
deep reflections on human thought and the nature of being. These concepts challenge
МЕДИЦИНА, ПЕДАГОГИКА И ТЕХНОЛОГИЯ:
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our understanding of existence, emphasizing the interplay between presence and
absence, and exploring the essence of reality itself.
In the mid-17th century, with the introduction of the coordinate system and the
number line into mathematics by P. Fermat and R. Descartes, zero was recognized as
a number. It was also proven that both positive and negative numbers correspond to
specific points on the number line, with zero serving as the central reference point. This
development provided a geometric interpretation of numbers, further solidifying zero's
role in mathematics.
In his 1783 work, L. Euler used the term
sifra
instead of zero. In 1799, K. Gauss
also adopted this term, and it continues to be used in England today. Starting from the
early 16th century, scholars in Germany and other countries began to use zero in its
current sense in their works. The recognition of zero as a number in mathematics was
based on the concept of subtracting a number from itself, i.e., writing "a – a = 0." This
recognition of zero as a number greatly facilitated arithmetic calculations.
In summary, zero is an integer. It is one of the digits in the decimal numeral
system. With its use, operations such as addition, subtraction, and multiplication can
be performed. However, division by zero is not possible. Since zero lies between two
odd numbers (-1 and 1) on the number line, it is considered an even number. (Abbos
Akmalov, Candidate of Pedagogical Sciences,
Tafakkur
Journal, Issue 1, 2020)
The concept of zero is one of humanity's most important discoveries. Initially
starting as a simple symbol, today it has become the foundation of the development of
science and technology. Throughout history, zero has evolved philosophically,
mathematically, and practically, leading to the scientific breakthroughs we have today.
Its impact spans across various fields, enabling advancements in mathematics, physics,
computing, and many other disciplines.
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МЕДИЦИНА, ПЕДАГОГИКА И ТЕХНОЛОГИЯ:
ТЕОРИЯ И ПРАКТИКА
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