Discontinuity (Real Analysis)/Examples/Example 2

Example of Discontinuity in the context of Real Analysis

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

$\forall x \in \R: \map f x = \begin {cases} \dfrac 1 k & : 0 \le x \le k \\ 0 & : \text {otherwise} \end {cases}$

Then $f$ has a discontinuity at $x = 0$ and $x = k$

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): discontinuity