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I The number zero

  1. Apr 16, 2016 #1
    Good morning,
    How do we prove that the number zero is a negative or positive number?
  2. jcsd
  3. Apr 16, 2016 #2


    Staff: Mentor

    Zero by definition is neither positive nor negative so there is no proof for it.

    Here's a brief discussion on Zero:

    from wikipedia:

  4. Apr 16, 2016 #3
    Why zero , in France , can be a negative or positive number?
    My reasoning:
    1) [tex]0>0[/tex] involves [tex]0=0+a[/tex] where [tex]a>0[/tex] and involves [tex]0+a>0+a[/tex] and [tex]a>a[/tex] and this is false.
    2) [tex]0<0[/tex] involves [tex]0=0-a[/tex] where [tex]a>0[/tex] and involves [tex]0-a<0-a[/tex] and [tex]-a<-a[/tex] and this is false.
    So the number zero can not be negative or positive.What was supposed to prove.My proof is correct?
  5. Apr 17, 2016 #4


    Staff: Mentor

    I doubt that this is correct. By definition of the terms negative and positive, zero is neither negative nor positive.
    You have started with a false assumption; i.e., that 0 is larger than itself. No finite number can be larger than itself, nor can it be smaller than itself.
    You're starting with a false assumption here, as well.

    From wikipedia, https://simple.wikipedia.org/wiki/Positive_number
    A positive number is a number that is bigger than zero.

    The definition for negative number is similar.
  6. Apr 17, 2016 #5


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    Science Advisor

    By another definition, zero is both negative and positive. I was taught to use the terms "strictly positive" and "strictly negative" in order to avoid the resulting potential for ambiguity. On the other hand, that class was some forty years ago and fashions may have changed.
  7. Apr 19, 2016 #6


    User Avatar
    Gold Member

    This fact

    or this

    doesn't convince me ...
  8. Apr 19, 2016 #7


    User Avatar
    Science Advisor
    Homework Helper

    (bolding mine)
    Probably the confusion is just a matter of definition.
    In the English Wikipedia, in the article about zero, one reads:
    In the French Wikipedia, in the article about zero, one reads:
    Translated, that says: "Zero is the only number that is real, positive, negative and purely imaginary".
    So, it really depends if by "positive" one means > 0, as the English Wikipedia does, or ≥ 0, as the French Wikipedia does.
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