Definition:Arabic Numerals
Definition
The Arabic numerals are:
\(\ds 1:\) | \(\)one\(:\) | \(\ds \circ\) | ||||||||||||
\(\ds 2:\) | \(\)two\(:\) | \(\ds \circ \, \circ\) | ||||||||||||
\(\ds 3:\) | \(\)three\(:\) | \(\ds \circ \circ \circ\) | ||||||||||||
\(\ds 4:\) | \(\)four\(:\) | \(\ds \circ \circ \circ \, \circ\) | ||||||||||||
\(\ds 5:\) | \(\)five\(:\) | \(\ds \circ \circ \circ \circ \circ\) | ||||||||||||
\(\ds 6:\) | \(\)six\(:\) | \(\ds \circ \circ \circ \circ \circ \, \circ\) | ||||||||||||
\(\ds 7:\) | \(\)seven\(:\) | \(\ds \circ \circ \circ \circ \circ \circ \circ\) | ||||||||||||
\(\ds 8:\) | \(\)eight\(:\) | \(\ds \circ \circ \circ \circ \circ \circ \circ \, \circ\) | ||||||||||||
\(\ds 9:\) | \(\)nine\(:\) | \(\ds \circ \circ \circ \circ \circ \circ \circ \circ \circ\) | ||||||||||||
\(\ds 0:\) | \(\)zero\(:\) | \(\ds \)or nought, naught, nil, nothing, cypher, zilch, kabutnik, sweet Fanny Adams, etc.\(\) |
They are used in conjunction with the positional decimal system of numeric representation: see Basis Representation Theorem.
Also known as
The Arabic numerals are also known as the Hindu-Arabic numerals.
An archaic name for the Arabic numerals is ciphers or cyphers.
Historical Note
The Arabic numerals were supposedly invented in the sphere of influence of the Arab culture in mediaeval times, but were in fact defined by Hindu mathematicians in approximately the $5$th or $6$th century CE.
Hence they are also referred to as Hindu-Arabic numerals or Hindu numerals.
They first arrived in Europe by way of the translation by Robert of Chester of Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala by Muhammad ibn Musa al-Khwarizmi.
However, the Arabic numeral system was slow to catch on, because of the general philosophical difficulty at the time with accepting the existence of the concept of zero. Also, important financial transactions and balances were at the time expressed in words, and so there appeared little need for $0$ by the banking and mercantile sectors.
It was not until the work of Leonardo Fibonacci, whose Liber Abaci (Book of Abacus or Book of Calculation) of $1202$ was highly influential, that this system of denoting numbers became popular throughout the Western world.
The Arabic numerals are referred to nowadays in antithesis to the Roman numerals, a cumbersome and limited technique for numeric expression which is still unaccountably and pointlessly used in the present day by some people and organizations for book chapter numbering, indexing and certain other more or less specialized purposes.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $0$ Zero
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Entry: cipher or cypher: 2.
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $0$ Zero
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: Hindu-Arabic numerals
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: Hindu-Arabic numerals
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $3$: Notations and Numbers: The Dark Ages?
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: Arabic numeral
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: number systems
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: numeral