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`

$f(x) < 0$**negative part**of the function $$f_-(x):=\cases{-f(x)&if`\\0&else.}$$`

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```Note that $f_+\ge 0$ and $f_-\ge 0$ and that $f=f_+-f_-$ as well as $|f|=f_++f_-.$

### Mentioned in:

Propositions: 1

### References

#### Bibliography

**Forster Otto**: "Analysis 1, Differential- und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983

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