Comments by "Sam Aronow" (@SamAronow) on "Why The Byzantines Spoke Greek Instead of Latin" video.

tl;dr The eastern part of the Roman Empire always had the bigger population, and Greek was already the main language there, or at least the common one. The fall of the west merely exacerbated this demographic fact.
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@Zingam If not Greek by identity than they likely spoke Greek as a common language, at least if educated. This was the case in Egypt, which was the most populous single province. So really it isn't so dissimilar from the status of English in the US.
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