That has no effect on history, and that is what we are talking about.
>The word "Jew" is an English word that did not come into existence until hundreds of years after the Bible was written. Your
statement that Judeans in Babylon did not receive the name Jews is completely meaningless.
History is never meaningless, except when attempts are made to "revise" it.
>After the failed revolt against Romans, Babylonia became the largest Jewish community in the world. Why was that? Because
there had been a large Jewish population there all along, since the captivity.
The word Jew (English equivalent) was attributed only to those who CAME OUT OF Babylon. (And subsequently those who the Jewish community accepted or acknowledged as Jews.) To that exent you are certainly correct.
>The second largest Jewish community was Egypt, where there had also been large numbers of Jews living since they fled there to escape Nebuchadnezzar's army in the 6th century BC. We know that there were Jews living there before the fall of Israel to the Romans, because historians tell us that the Septuagint was widely distributed to Jews in Egypt.
These were initially Judeans, not Jews. By definition. The word "Jew" as we know it today in English was a specific designation given only to those who returned to Jerusalem at the END of the Babylonian captivity.
>The diaspora did not begin when Israel fell to the Romans. It had already existed for centuries.
The Southern Kingdom diaspora began with the Babylonian captivity. The Northern Kingdom diaspora began with the Assyrian captivity. My interest is almost entirely in the Northern Kingdom. So with the clarifications given above I will close with the same statement which caused you to take issue:
Since only ~50,000 Judeans returned from Babylon, that leaves another half million unaccounted for. Technically they are not Jews since only those who returned from Babylon were accorded that name, but they certainly were Judeans, and essentially the same people.
There is no evidence that the Jews who returned to Israel thought of the ones who stayed behind in Babylonia (and the ones in Egypt) as anything but EXACTLY the same people as themselves. Your attempt to make a distinction between Jews and Judeans is silly because the language of the time made no such distinction.
FYI, it is believed that the synagogue was invented in Babylonia during the captivity and so there was some sort of Jewish religious practice going on in Babylonia between the captivity and the time many Jews from Israel returned there after the failed revolt against the Romans.