Word Count : 416

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To prove that the function \( f(x) \) given by: \[ f(x) = \begin{cases} 2, & \text{if } x \text{ is irrational} \\ -2, & \text{if } x \text{ is rational} \end{cases} \] is discontinuous at every \( x \in \mathbb{R} \), we use the sequential definition of continuity. ### Sequential Definition of Continuity A function \( f \) is continuous at a point \( c \) if for ____ ____ _______ ______ ________ __________ ________ ________ ___.
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