Also, I admire the criticism of the people in that thread, but given the right adjectives, there is really no problem with what was said. I think that if you replace "entire" with "holomorphic over domain D" (where D is the complex plane minus any singularities or branch cuts) and suffix "unique" with "unique up to branch choice" (or state some property that only the principal branch has) then we might get better responses, and certainly more clarity.
Andrew Robbins
Andrew Robbins