◀ ▲ ▶Branches / Analysis / Definition: Positive and Negative Parts of a Real-Valued Function
Definition: Positive and Negative Parts of a Real-Valued Function
Let $D$ be a real interval and $f:D\to\mathbb R$ a function. Using the order-relation for real numbers, we define:
- the positive part of the function $$f_+(x):=\cases{f(x)&if$f(x) > 0$
\\0&else.}$$
- the negative part of the function $$f_-(x):=\cases{-f(x)&if$f(x) < 0$
\\0&else.}$$
Note that $f_+\ge 0$ and $f_-\ge 0$ and that $f=f_+-f_-$ as well as $|f|=f_++f_-.$
Mentioned in:
Propositions: 1
Thank you to the contributors under CC BY-SA 4.0! 
- Github:
-
References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
