It is generally alleged that Einstein's theory leads to a finite but unbounded universe. This allegation stems from an incorrect analysis of the metric for the point-mass when the lambda-term is non-zero. The standard analysis has incorrectly assumed that the variable r denotes a radius in the gravitational field. Since r is in fact nothing more than a real-valued parameter for the actual radial quantities in the gravitational field, the standard interpretation is erroneous. Moreover, the true radial quantities lead inescapably to zero lambda-term so that, cosmologically, Einstein's theory predicts an infinite, static, empty universe.