"Much greater," denoted 
, indicates a strong
inequality in which 
is not only greater than 
, but much greater according to some convention.
For an astronomer, "much" may mean by a factor of 100 (or even 10), while
for a mathematician, it might mean by a factor of 
(or even much more).
In number theory, 
also denotes a lower bound in Vinogradov
notation. For positive functions 
and 
, 
means that 
for some constant 
throughout the specified range.
Euclid used the terminology that if 
is greater than 
and 
is greater than 
, then 
is said to be much (or far) greater than 
. In that sense, "far greater than" is synonymous
with "greater than" for a dense set of ordered quantities.
