Why does the degeneracy discriminant z<<1 fail at high temperature?

[hokhani]

The degeneracy discriminant, that specifies the requirement for applicability of classical Maxwell-Blotzman statistics, is z<<1 where z is fugacity and $z=exp^(\mu/kT)$. However when $T\to \infty$ we would have $z\to 1$ which means we are in quantum regime while it is obvious that we are in classical regime at high temperatures. And there is also such a discrepancy when $T\to 0$. Could anyone please guide me?

 

[DrClaude]

I'm not sure where you got the condition $z \ll 1$ from. See http://en.wikipedia.org/wiki/Maxwell–Boltzmann_statistics#Limits_of_applicability