Bound Variable/Examples/Algebraic Example

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Example of Bound Variable

In algebra:

$x^2 + 2 x y + y^2 = \paren {x + y}^2$

both $x$ and $y$ are bound variables.

This is illustrated in considering the full formal statement:

$\forall x : \forall y : \paren {x^2 + 2 x y + y^2 = \paren {x + y}^2}$

where each occurrence of $x$ and $y$ is bound by a quantifier.