  It is a common impression that by only setting the maximum occupation number
to infinity, which is the demand of the indistinguishability of bosons, one can
achieve the statistical distribution that bosons obey -- the Bose-Einstein
distribution. In this letter, however, we show that only with an infinite
maximum occupation number one cannot uniquely achieve the Bose-Einstein
distribution, since in the derivation of the Bose-Einstein distribution, the
problem of iterated limit is encountered. For achieving the Bose-Einstein
distribution, one needs to take both the maximum occupation number and the
total number of particles to infinities, and, then, the problem of the order of
taking limits arises. Different orders of the limit operations will lead to
different statistical distributions. For achieving the Bose-Einstein
distribution, besides setting the maximum occupation number, we also need to
state the order of the limit operations.
