The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation.
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any non-negative integer using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, a numeral is not clearly distinguished from the number that it represents.
0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently division by zero has no meaning in arithmetic.
The Egyptian language, or Ancient Egyptian is an extinct branch of the Afro-Asiatic languages that was spoken in ancient Egypt. It is known today from a large corpus of surviving texts, which were made accessible to the modern world following the decipherment of the ancient Egyptian scripts in the early 19th century.
Ancient Egyptian hieroglyphs were the formal writing system used in Ancient Egypt for writing the Egyptian language. Hieroglyphs combined ideographic, logographic, syllabic and alphabetic elements, with more than 1,000 distinct characters. Cursive hieroglyphs were used for religious literature on papyrus and wood. The later hieratic and demotic Egyptian scripts were derived from hieroglyphic writing, as was the Proto-Sinaitic script that later evolved into the Phoenician alphabet. Egyptian hieroglyphs are the ultimate ancestor of the Phoenician alphabet, the first widely adopted phonetic writing system. Moreover, owing in large part to the Greek and Aramaic scripts that descended from Phoenician, the majority of the world's living writing systems are descendants of Egyptian hieroglyphs—most prominently the Latin and Cyrillic scripts through Greek, and the Arabic and Brahmic scripts through Aramaic.
The Phoenician alphabet is an abjad used across the Mediterranean civilization of Phoenicia for most of the 1st millennium BC. It was one of the first alphabets, and attested in Canaanite and Aramaic inscriptions found across the Mediterranean region. In the history of writing systems, the Phoenician script also marked the first to have a fixed writing direction—while previous systems were multi-directional, Phoenician was written horizontally, from right to left. It developed directly from the Proto-Sinaitic script used during the Late Bronze Age, which was derived in turn from Egyptian hieroglyphs.
Hieratic is the name given to a cursive writing system used for Ancient Egyptian and the principal script used to write that language from its development in the third millennium BCE until the rise of Demotic in the mid-first millennium BCE. It was primarily written in ink with a reed brush on papyrus.
Sexagesimal, also known as base 60, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates.
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, is a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world. For ordinary cardinal numbers, however, modern Greece uses Arabic numerals.
Theta uppercase Θ or ϴ; lowercase θ or ϑ; Ancient Greek: θῆταthē̂ta ; Modern: θήταthī́ta ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals, it has a value of 9.
An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction above sums to . Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including and as summands, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation. However, Egyptian fractions continue to be an object of study in modern number theory and recreational mathematics, as well as in modern historical studies of ancient mathematics.
Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt c. 3000 to c. 300 BCE, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions. Evidence for Egyptian mathematics is limited to a scarce amount of surviving sources written on papyrus. From these texts it is known that ancient Egyptians understood concepts of geometry, such as determining the surface area and volume of three-dimensional shapes useful for architectural engineering, and algebra, such as the false position method and quadratic equations.
Brahmi numerals are a numeral system attested in the Indian subcontinent from the 3rd century BCE. It is the direct graphic ancestor of the modern Hindu–Arabic numeral system. However, the Brahmi numeral system was conceptually distinct from these later systems, as it was a non-positional decimal system, and did not include zero. Later additions to the system included separate symbols for each multiple of 10. There were also symbols for 100 and 1000, which were combined in ligatures with the units to signify 200, 300, 2000, 3000, etc. In computers, these ligatures are written with the Brahmi Number Joiner at U+1107F.
Demotic is the ancient Egyptian script derived from northern forms of hieratic used in the Nile Delta. The term was first used by the Greek historian Herodotus to distinguish it from hieratic and hieroglyphic scripts. By convention, the word "Demotic" is capitalized in order to distinguish it from demotic Greek.
The Hindu–Arabic numeral system is a positional base-ten numeral system for representing integers; its extension to non-integers is the decimal numeral system, which is presently the most common numeral system.
In mathematics, ancient Egyptian multiplication, one of two multiplication methods used by scribes, is a systematic method for multiplying two numbers that does not require the multiplication table, only the ability to multiply and divide by 2, and to add. It decomposes one of the multiplicands into a set of numbers of powers of two and then creates a table of doublings of the second multiplicand by every value of the set which is summed up to give result of multiplication.
Cursive hieroglyphs, or hieroglyphic book hand, are a form of Egyptian hieroglyphs commonly used for handwritten religious documents, such as the Book of the Dead. This style of writing was typically written with ink and a reed brush on papyrus, wood, or leather. It was particularly common during the Ramesside Period, and many famous documents, such as the Papyrus of Ani, use it. It was also employed on wood for religious literature such as the Coffin Texts.
Modern Arabic mathematical notation is a mathematical notation based on the Arabic script, used especially at pre-university levels of education. Its form is mostly derived from Western notation, but has some notable features that set it apart from its Western counterpart. The most remarkable of those features is the fact that it is written from right to left following the normal direction of the Arabic script. Other differences include the replacement of the Greek and Latin alphabet letters for symbols with Arabic letters and the use of Arabic names for functions and relations.
An alphabetic numeral system is a type of numeral system. Developed in classical antiquity, it flourished during the early Middle Ages. In alphabetic numeral systems, numbers are written using the characters of an alphabet, syllabary, or another writing system. Unlike acrophonic numeral systems, where a numeral is represented by the first letter of the lexical name of the numeral, alphabetic numeral systems can arbitrarily assign letters to numerical values. Some systems, including the Arabic, Georgian and Hebrew systems, use an already established alphabetical order. Alphabetic numeral systems originated with Greek numerals around 600 BC and became largely extinct by the 16th century. After the development of positional numeral systems like Hindu–Arabic numerals, the use of alphabetic numeral systems dwindled to predominantly ordered lists, pagination, religious functions, and divinatory magic.
