Definition:Discontinuity (Real Analysis)/Finite

From ProofWiki
Jump to navigation Jump to search


Let $X \subseteq \R$ be a subset of the real numbers.

Let $f: X \to \R$ be a real function.

Let $f$ be discontinuous at $c \in X$.

$f$ is a finite discontinuity on $f$ if and only if $\map f c$ is finite.


Example 1

Let $f: \R \to \R$ be the real function defined as:

$\forall x \in \R: \map f x = \map \cos {\dfrac 1 x}$

Then $f$ has a finite discontinuity at $x = 0$ which is non-removable.

Also see

  • Results about finite discontinuities can be found here.