[throwawaylolx]

The emperor of "Byzantium" literally was the emperor of the Roman empire; it was not merely a claim like in the other cases but an administrative and historical fact. It is more accurate to say that "the Byzantine Empire" not being the actual Roman empire is merely a modern claim.

[toyg]

Well, technically it was one of two emperors.

[epolanski]

Yes and no as the emperor Constantine literally moved the capital from Rome to Costantinople and Constantinople was the capital of both empires for another few centuries till the death of Giustiniano.

https://en.wikipedia.org/wiki/Constantinople

[thaumasiotes]

> The emperor of "Byzantium" literally was the emperor of the Roman empire; it was not merely a claim like in the other cases but an administrative and historical fact.

Not in any useful sense.

Cyrus the Great was literally the King of Sumer and Akkad. Did he know where Akkad was?

Tsai Ing-wen is literally the President of China. You might object that China doesn't even have a president, but the administrative and historical facts are against you.

[retrac]

If the United States were invaded on the east coast, and the invaders were stopped at the Mississippi, and the US then carried on with its capital in Sacramento for the next 1000 years, do you think the executive would no longer be called the President of the United States just because the US lost some of the states? (Credit to Dan Carlin for that little thought experiment.)

The Byzantines called themselves Roman. They thought of themselves as Roman. To them, the constitution of their political order dated to 753 BC with the founding of Rome, even after they lost Rome. It wasn't just a label. For example, Latin remained is use in law in the empire, many hundreds of years after they lost the west. Emperor Heraclius around 610 AD would undertake a project to start translating all the old Latin laws into Greek (even though he may have spoke Latin himself natively). If nothing else, the Roman self-identity is important for understanding how they saw themselves in their own historiography.