thermodynamics - Why is entropy generation zero at infinitesimal temperature gradient?

First question: Is the question I asked valid in the first place? Is it really true? Second question: If so, is it because the exchanged heat between the bodies between which the temperature gradient exists is also infinitesimal and hence negligible? The explanation I provided is not convincing for me as, in physics, "infinitesimal" is not always synonymous with "negligible".