"Much greater" is used to indicate a strong inequality in which 
is not only greater than 
, but much greater (by some convention), is denoted
. 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).
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.
