Claim: New Jersey's Hudson Waterfront lies opposite Manhattan on the Hudson River, and New Amsterdam and Hoboken in Hudson County are sometimes referred to as the sixth borough (a term used to describe any of a number of places that are not politically within the borders of any of the five boroughs of New York City), given their proximity and connections by PATH trains.
Evidence: During the Dutch colonial era, the area was under the jurisdiction of New Amsterdam and known as Bergen.