Positive And Negative Parts

(Elementary Mathematic)

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Elementary Mathematic
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What is Positive and negative parts?

In mathematics, the positive part of a real or extended real-valued function is defined by the formula Intuitively, the graph of is obtained by taking the graph of , chopping off the part under the x-axis, and letting take the value zero there. Similarly, the negative part of f is defined as Note that both f+ and f− are non-negative functions. A peculiarity of terminology is that the 'negative part' is neither negative nor a part (like the imaginary part of a complex number is neither imaginary nor a part). The function f can be expressed in terms of f+ and f− as Also note that . Using these two equations one may express the positive and negative parts as Another representation, using the Iverson bracket is One may define the positive and negative part of any function with values in a linearly ordered group.

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elementary mathematic

Synonyms

Negative partPositive part

Translations

Parte positiva e parte negativa di una funzione (it)Partie positive et partie négative d'une fonction (fr)Positivteil und Negativteil einer reellwertigen Funktion (de)正成分と負成分 (ja)

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