Since the total probability to find the system in some microstate (the sum of all p i) must be equal to 1, we know that the constant of proportionality must be the normalization constant, and so, we can define the partition function to be this constant: Z = ∑ ∑ i e − − β β E i = Ω Ω ( S , B ) ( E ) Ω Ω B ( E ) .