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It is given that

n(ε)=g(ε)f(ε) Here ε is the energy state.

where according to my understanding

n(ε)=number of particles which are present in an energy state ε.

g(ε)=number of states corresponding to energy state ε.

f(ε)=average number of particles in each state.

Is my understanding right? I can't figure this out.

In the next two lines he states that if the energy distribution is continous rather than discrete, then..

1.The number of energy states between ε and ε+dε(dεis small change in energy) is g(ε)dε.My question is how is this possible? If there are two states, ε and ε+dε. then the number of states between them is g(ε+dε)-g(ε), is it not?

2. The same is said for number number of particles between ε and ε+dε. He says that the number is equal to n(ε)dε,How? Should it not be like g(ε+dε)-g(ε)??

He uses these two assumptions to derive the Maxwell-Boltzmann distribution(We don't derive partition function). Please help me out as I need atleast some basic level of understanding(if not rigorous)..