Okay, yeah you make a good point. Strictly speaking a logarithmic function does not imply a convergent series. To be more precise, what I'm talking about are sl

Okay, yeah you make a good point. Strictly speaking a logarithmic function does not imply a convergent series. To be more precise, what I'm talking about are slowly varying functions. These are functions which don't converge but which have similar characteristics to convergent functions (namely, extremely slow rate of change). Since you made the correction you're probably already familiar with these, but for the benefit of others: https://en.wikipedia.org/wiki/Slowly_varying_function https://en.wikipedia.org/wiki/Slowly_varying_function