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The two following symbols are called quantifyers: If $ p$ is some specific property, the sentence $ \forall x , \; p(x)$ means that ``for every $ x$, the property $ p$ holds. If $ p$ is a property for pairs of objects, the sentence $ \forall x, \; \exists y \; \vert \; p(x,y)$ means that for every $ x$, there exists at least one $ y$ such that $ p$ holds for $ x$ and $ y$.

Note 1   The reader understood alreday that the vertical bar $ \vert$ means ``such that''. Sometimes we use a semicolon ``;'' instead of $ \vert$.

root 2002-06-10