Definition:Finite Discontinuity
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Definition
Let $A \subseteq \R$ be a subset of the real numbers.
Let $f: A \to \R$ be a real function.
Let $f$ be discontinuous at $a \in A$.
The point $a$ is a finite discontinuity of $f$ if and only if either:
- $(1): \quad a$ is a removable discontinuity
or:
- $(2): \quad a$ is a jump discontinuity.