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RE: [PrimeNumbers] Positive / negative zero

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  • Paul Leyland
    ... Ah, another question which has my favourite answer: it depends. The IEEE floating point standard has an encoding where the two infinities are distinguished
    Message 1 of 3 , Dec 1, 2001
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      > If there is a positive infinity and a negative infinity, isn't there a
      > positive zero and a negative zero, the reciprocals of the infinities?

      Ah, another question which has my favourite answer: it depends.

      The IEEE floating point standard has an encoding where the two
      infinities are distinguished by having a one-bit difference between
      them: the sign bit. In this mode, there are two encodings of zero
      which are distinguished in the same way. The obvious identities are
      then preserved when doing arithmetic on these quantities. However, -0
      compares equal to +0 and an interesting philosophical question arises as
      to how they differ when they are equal!

      In mathematics, we often come across limits which are taken as some
      quantity tends to zero from above or below. These limiting values could
      reasonably be taken as definitions of +0 and -0. Although the limiting
      values themselves are equal, the limiting values of the expression need
      not be the same or, for that matter, equal to the value of the
      expression at zero. For an example, consider the sign(x) function which
      is -1 for negative x, 0 for x=0 and +1 for positive x.


      Paul
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