"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.

See also

Greater, Much Less, Vinogradov Notation

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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Much Greater

Cite this as:

Weisstein, Eric W., with contributions by Richard Carr. "Much Greater." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MuchGreater.html

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