  We define covering and separation numbers for functions. We investigate their
properties, and show that for some classes of functions there is exact equality
of separation and covering. We provide analogues for various geometric
inequalities on covering numbers, such as volume bounds, bounds connected with
Hadwiger's conjecture, and inequalities about M-positions for geometric
log-concave functions. In particular, we obtain strong versions of M-positions
for geometric log-concave functions.
