In Unicode, why are there two representations for the Arabic digits?

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According to the code charts, U+0660 .. U+0669 are ARABIC-INDIC DIGIT values 0 through 9, while U+06F0 .. U+06F9 are EXTENDED ARABIC-INDIC DIGIT values 0 through 9.

In the Unicode 3.0 book (5.2 is the current version, but these things don’t change much once set), the U+066n series of glyphs are marked ‘Arabic-Indic digits’ and the U+06Fn series of glyphs are marked ‘Eastern Arabic-Indic digits (Persian and Urdu)’.
It also notes:

  • U+06F4 – ‘different glyphs in Persian and Urdu’
  • U+06F5 – ‘Persian and Urdu share glyph different from Arabic’
  • U+06F6 – ‘Persian glyph different from Arabic’
  • U+06F7 – ‘Urdu glyph different from Arabic’

For comparison:

  • U+066n: ٠١٢٣٤٥٦٧٨٩
  • U+06Fn: ۰۱۲۳۴۵۶۷۸۹

Or, enlarged by making the information into a title:

U+066n: ٠١٢٣٤٥٦٧٨٩

U+06Fn: ۰۱۲۳۴۵۶۷۸۹

Or:

     U+066n    U+06Fn
0      ٠         ۰
1      ١         ۱
2      ٢         ۲
3      ٣         ۳
4      ٤         ۴
5      ٥         ۵
6      ٦         ۶
7      ٧         ۷
8      ٨         ۸
9      ٩         ۹

(Whether you can see any of those, and how clearly they are differentiated may depend on your browser and the fonts installed on your machine as much as anything else. I can see the difference on 4 and 6 clearly; 5 looks much the same in both.)

Based on this information, if you are working with Arabic from the Middle East, use the U+066n series of digits; if you are working with Persian or Urdu, use the U+06Fn series of digits. As a Unicode application, you should accept either set of codes as valid digits (but you might look askance at a sequence that mixed the two sets of digits – or you might just leave well alone).

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