Q:

Lesser number vs. smaller number

I am wondering about the correct use of lesser/smaller in the following phrase:

This library has a smaller/lesser number of books than the National Library.

I did find another thread on nearly the same question, where one answer states: "As a general rule, 'smaller' is used for size, whereas 'lesser' is used for quantity." In this particular example, however, I am not quite sure how to approach this, as 'number' in this sentence refers to an amount, which you could argue has a size, and 'smaller/lesser number' as a whole only refers to a quantity. 
To me, 'a smaller number' sounds better, but I am not a native speaker and I can't make out a clear reason for choosing one over the other.

A:

The meaning is clear in either case, as long as you say 'smaller number', not just 'smaller', as that would imply the sizes of the books were smaller.
However if it were me I wouldn't use either of them. I would say:
'This library has fewer books than the National Library.'  

