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Revision difference : well-defined |
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A mathematical concept is {\em well-defined} (German {\em wohldefiniert}, French {\em bien d\'efini}), if its contents in \PMlinkescapetext{independent} on the form or the alternative representative which is used for defining it.
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A mathematical concept is {\em well-defined} (German {\em wohldefiniert}, French {\em bien d\'efini}), if its contents in \PMlinkescapetext{independent} on the form or the alternative representant which is used for defining it.
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| For example, in defining the \PMlinkname{power}{FractionPower} $x^r$ with $x$ a positive real and $r$ a rational number, we can freely choose the fraction form $\frac{m}{n}$ ($m\in\mathbb{Z}$,\, $n\in\mathbb{Z}_+$) of $r$ and take |
For example, in defining the \PMlinkname{power}{FractionPower} $x^r$ with $x$ a positive real and $r$ a rational number, we can freely choose the fraction form $\frac{m}{n}$ ($m\in\mathbb{Z}$,\, $n\in\mathbb{Z}_+$) of $r$ and take |
| $$x^r := \sqrt[n]{x^m}$$ |
$$x^r := \sqrt[n]{x^m}$$ |
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and be sure that the value of $x^r$ does not depend on that choice (this is justified in the entry fraction power). So, the $x^r$ is well-defined.
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and be sure that the value of $x^r$ does not depend on that choise (this is justified in the entry fraction power). So, the $x^r$ is well-defined.
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