1. The problem statement, all variables and given/known data So the transition temperture is defined when at a given temperture the mean number of particles in the lowest state is 0. So does that imply there are tempertures where the mean value is a negative number? 3. The attempt at a solution If not than surely at 1000k, the mean number in the lowest state is still 0 so there is no unique transition temperture. However this problem is overcome by setting T=0 which would mean the number of particles in the ground state must increase. So when it is 0, it will be the start of the occupation of the ground state as it can only increase because we have set T=0 in order to calculate the zeta function.