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 .
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| - Positivteil und Negativteil einer reellwertigen Funktion (de)
- Parte positiva e parte negativa di una funzione (it)
- Partie positive et partie négative d'une fonction (fr)
- 正成分と負成分 (ja)
- Positive and negative parts (en)
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| - Als Positivteil und Negativteil einer reellwertigen Funktion bezeichnet man in der Mathematik zwei dieser Funktion zugeordnete spezielle Funktionen. Anschaulich stimmt der Positivteil mit der eigentlichen Funktion überein, wenn diese positive Werte annimmt und ist ansonsten null. Analog wird der Negativteil einer Funktion definiert. (de)
- En mathématiques, à toute fonction réelle f, on peut associer deux fonctions positives, sa partie positive f+ et sa partie négative f−, définies respectivement par : Malgré son nom, la « partie négative » est donc positive. Intuitivement, le graphe par exemple de la partie positive est obtenu en tronquant le graphe de f quand il passe sous l'axe des abscisses, c'est-à-dire encore en posant 0 en ces points et en laissant inchangé le reste du graphe. (fr)
- In matematica, per ogni funzione reale si possono definire due funzioni "componenti", dette parte positiva e parte negativa della funzione, date rispettivamente da Intuitivamente, il grafico per esempio della parte positiva è ottenuto troncando il grafico di quando esso passa sotto l'asse delle ascisse, ponendolo a 0 in quei punti e lasciando inalterato il resto. Una peculiarità della definizione è che la "parte negativa" non è negativa, anzi, è ovunque positiva o al più nulla. La scomposizione di una funzione qualsiasi in due funzioni sempre non negative si rivela utile in determinati casi. (it)
- 数学における実または拡大実数値函数の正成分（せいせいぶん、英: positive part）および負成分（ふせいぶん、英: negative part）は、その函数から定まる二つの特定の非負値函数である。 元の函数が正の値を取る場合、その正成分は元の函数と同じ値を取り、元の函数がそれ以外の値を取る場合、正成分は 0 を値とする。負成分も同様に、元の函数が負の値を取る場合、その負成分は元の函数の値と大きさが等しく符号だけ異なる正の値を取り、元の函数がそれ以外の値を取る場合、負成分は 0 を値とする。 より一般に、全順序群に値をとる任意の函数に対して正成分と負成分の概念は定義できるということに注意せよ。 (ja)
- 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 . (en)
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| - Als Positivteil und Negativteil einer reellwertigen Funktion bezeichnet man in der Mathematik zwei dieser Funktion zugeordnete spezielle Funktionen. Anschaulich stimmt der Positivteil mit der eigentlichen Funktion überein, wenn diese positive Werte annimmt und ist ansonsten null. Analog wird der Negativteil einer Funktion definiert. (de)
- En mathématiques, à toute fonction réelle f, on peut associer deux fonctions positives, sa partie positive f+ et sa partie négative f−, définies respectivement par : Malgré son nom, la « partie négative » est donc positive. Intuitivement, le graphe par exemple de la partie positive est obtenu en tronquant le graphe de f quand il passe sous l'axe des abscisses, c'est-à-dire encore en posant 0 en ces points et en laissant inchangé le reste du graphe. (fr)
- 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. The unit ramp function is the positive part of the identity function. (en)
- In matematica, per ogni funzione reale si possono definire due funzioni "componenti", dette parte positiva e parte negativa della funzione, date rispettivamente da Intuitivamente, il grafico per esempio della parte positiva è ottenuto troncando il grafico di quando esso passa sotto l'asse delle ascisse, ponendolo a 0 in quei punti e lasciando inalterato il resto. Una peculiarità della definizione è che la "parte negativa" non è negativa, anzi, è ovunque positiva o al più nulla. La scomposizione di una funzione qualsiasi in due funzioni sempre non negative si rivela utile in determinati casi. (it)
- 数学における実または拡大実数値函数の正成分（せいせいぶん、英: positive part）および負成分（ふせいぶん、英: negative part）は、その函数から定まる二つの特定の非負値函数である。 元の函数が正の値を取る場合、その正成分は元の函数と同じ値を取り、元の函数がそれ以外の値を取る場合、正成分は 0 を値とする。負成分も同様に、元の函数が負の値を取る場合、その負成分は元の函数の値と大きさが等しく符号だけ異なる正の値を取り、元の函数がそれ以外の値を取る場合、負成分は 0 を値とする。 より一般に、全順序群に値をとる任意の函数に対して正成分と負成分の概念は定義できるということに注意せよ。 (ja)
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