I've seen two different definitions for the f-number of a general-purpose lens. Are they consistent ?

I'm assuming that subjects are distant (not macro, magnification is small), and we have a lens corrected for coma and spherical aberration.

I mean f-number in the sense that it indicates the brightness of a lens which has no internal losses.

The 1/(2 * Numerical_Aperture) definition leads to f/0.5 as a limit; the f/D definition does not.

I was looking at: https://books.google.it/books?id=UY6QzgzgieYC&lpg=PP1&dq=nakamura%20The%20F-number%20of%20a%20lens%20(%20F%20)%20is%20expressed%20as%20half%20the%20opening%20angle&hl=it&pg=PA25#v=onepage&q=The%20F-number%20of%20a%20lens&f=false