Category:Definitions/Removable Discontinuities (Real Analysis)
Jump to navigation
Jump to search
This category contains definitions related to removable discontinuities in the context of real analysis.
Related results can be found in Category:Removable Discontinuities (Real Analysis).
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 $c \in X$.
Definition 1
The point $c$ is a removable discontinuity of $f$ if and only if the limit $\ds \lim_{x \mathop \to c} \map f x$ exists.
Definition 2
The point $c$ is a removable discontinuity of $f$ if and only if there exists $b \in \R$ such that the function $f_b$ defined by:
- $\map {f_b} x = \begin {cases} \map f x &: x \ne c \\ b &: x = c \end {cases}$
is continuous at $c$.
Pages in category "Definitions/Removable Discontinuities (Real Analysis)"
The following 4 pages are in this category, out of 4 total.