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Contrary to the standard δN formalism, in which we fix the final time of inflation and we count backward in time, the δn formalism fixes an initial time and count forward in time. In this talk I will show that both formalisms are exactly equivalent, being the latter much more convenient to compute the probability distribution function of the non-linear comoving curvature fluctuation at the end of inflation, whose precise knowledge is of crucial importance for PBH formation.