1. The problem statement, all variables and given/known data In stat physics, the multiplicity function is discrete but to find the max value, you can assume it is continous around the max region hence use calculus. Why is it legimate to do that? That is approximate a discrete function as continous? 3. The attempt at a solution Is it because we are talking about large n values or number of particles of the order of 10^23. So to discretely plot this graph on an observable scale, it would be huge so we map it into a smaller graph so that the points are more dense together hence is more justified to use calculus. But is this argument a bit loose?