Category:Definitions/Discontinuities of the First Kind
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This category contains definitions related to Discontinuities of the First Kind.
Related results can be found in Category:Discontinuities of the First Kind.
Let $X$ be an open subset of $\R$.
Let $f: X \to Y$ be a real function.
Let $f$ be discontinuous at some point $c \in X$.
Definition 1
$c$ is known as a discontinuity of the first kind of $f$ if and only if:
- $\ds \lim_{x \mathop \to c^-} \map f x$ and $\ds \lim_{x \mathop \to c^+} \map f x$ exist
where $\ds \lim_{x \mathop \to c^-} \map f x$ and $\ds \lim_{x \mathop \to c^+} \map f x$ denote the limit from the left and limit from the right at $c$ respectively.
Definition 2
$c$ is known as a discontinuity of the first kind of $f$ if and only if either:
- $c$ is a jump discontinuity
or:
- $c$ is a removable discontinuity.
Pages in category "Definitions/Discontinuities of the First Kind"
The following 10 pages are in this category, out of 10 total.
D
- Definition:Discontinuity (Real Analysis)/First Kind
- Definition:Discontinuity (Real Analysis)/Jump
- Definition:Discontinuity (Real Analysis)/Removable
- Definition:Discontinuity (Real Analysis)/Simple
- Definition:Discontinuity of the First Kind/Also known as
- Definition:Discontinuity of the First Kind/Definition 1
- Definition:Discontinuity of the First Kind/Definition 2