"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.
See also
Portions of this entry contributed by Richard Carr
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References
Heath, T. L. The Thirteen Books of the Elements, 2nd ed., Vol. 3: Books X-XIII. New York: Dover, 1956.
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Cite this as:
Carr, Richard and Weisstein, Eric W. "Much Greater." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MuchGreater.html