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Multiplicative modulus

  1. Jun 1, 2009 #1
    "multiplicative modulus"

    I have found a multiplicative modulus function, an analogue of absolute value for multiplication. Not a groundbreaking one, i'm sure someone has thought about this before. More specifically it is a function that satisfies:

    [tex]\operatorname{MM}(1) = 1[/tex]
    [tex]\operatorname{MM}(x^{-1}) = \operatorname{MM}(x)[/tex]
    [tex]| \log{x} | = \log{(\operatorname{MM}(x))} \, \forall x \in \mathbb{R}^+[/tex]
    [tex]\operatorname{MM}(x) = x \, \forall x \ge 1 [/tex]
    [tex]\operatorname{MM}^{-1} (x) = x^{\pm 1}[/tex]

    Why isn't this function widely used in mathematics? is it because it can be replaced with [tex]e^{|\ln{x}|}[/tex] ?
  2. jcsd
  3. Jun 1, 2009 #2

    matt grime

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    Re: "multiplicative modulus"

    May I simplify?

    We define a function on the strictly positive real numbers:

    f(x)=x if x >=1,
    f(x)=1/x otherwise.

    It probably isn't widely used because no one has needed to use it.
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