# Confused about the Pauli exclusion principle

I've been struggling to understand this: Let's say I have a gas of one million electrons. Does every single one of those electrons have a different energy (up to the degeneracy from the different momentum components)?

Avogadro constant, which is a good estimate of the order of magnitude for a macroscopic number of particles, is much bigger than a million ($$N_A\approx 10^{23}$$). Yet, there is nothing difficult in giving every pair of electrons (with different spins) their own momentum state, for momentum is continuous - i.e., the number of available states is infinite.