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Wikipedia says about Byzantine emperor Heraclius that he was responsible for "introducing Greek as the Eastern Empire's official language".

If so, is it right to assume that Byzantines used Roman numerals up to that point, and then after Heraclius, Greek numerals?

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    They tried Byzantine numerals but decided they were too Byzantine. Commented Jan 19, 2016 at 18:09

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They used both. On coins often you can find the denomination in Greek, but the date in Roman numerals. As a general rule, all dates and day numbers were in Roman numerals. Also, it was customary for common accounts and ledgers to be kept in Roman numerals. Greek numbers were mostly used in literary contexts, like books on mathematics.

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