Yes, it would be a sunday to a Jew, but still Saturday to a Roman!
That is the essence of this ancient error. - The writings in the gospels were at first to mainly Jews, so the terms used were in the cultural vernacular of the Jew.
It was the “first of the sabbaths,” a clear plural, that was misunderstood by the English translators that were not knowledgeable on many colloquial expressions that were in the gospels. They thus failed to understand that what was being addressed was Pentecost specifically, and not just a day of the week.
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I just looked that up from different sites it seems the experts have different opinions on that issue. But never the less what an interesting subject.