Notation for the relationship $a > b, \forall a \in A, \forall b \in B$ for the sets $A, B$

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I encountered the relationship

$$ a > b, \forall a \in A, \forall b \in B $$

Is there any notation for the relationship between the sets $A$ and $B$? Can I say $A > B$?

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Define $$ A>B\ :\Leftrightarrow\ \forall a\in A,\forall b\in B, a>b$$ and beginning with the line after that definitioin you can use it.