Answer:
It may seem peculiar to think of ethnic Greeks (as well as other groups) designating themselves as Romans, or Romaioi so long after both the Roman and Byzantine empires had disappeared, but the apparent oddity of this fact is largely a product of the conventions for naming and distinguishing certain historical groups. The inhabitants of the later eastern Roman Empire are called Byzantines by us, but in their own time they would have referred to themselves, and been referred to by others, as Romans. In our perception the Byzantine Empire eventually evolved to become an entity separate from the Roman Empire which preceded and originated it, but that evolution was not problematic, or perhaps not even apparent, for those living within the empire during any of its iterations. For them it was still the Roman empire, and their culture was still Roman as well. It may seem odd that, for example, an ethnic Greek and Orthodox Christian inhabitant of Ottoman Anatolia in the 19th century could call themselves by the same name as a Latin-speaking pagan inhabitant of Italy in the classical period. It is clear, however, that while historians might neatly delineate historical periods and people groups, those delineations must often overlook the persistent continuity of many aspects of culture; a name, a religion, or even an ethos can survive long after we might suspect.
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