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Math Help - Do you consider zero to be a whole number? Positive or negative?

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    Question Do you consider zero to be a whole number? Positive or negative?

    Do you consider zero to be a whole number? Positive or negative?
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    Re: Do you consider zero to be a whole number? Positive or negative?

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    Re: Do you consider zero to be a whole number? Positive or negative?

    Quote Originally Posted by mash View Post
    Do you consider zero to be a whole number? Positive or negative?
    There is no universal agreement on the answer to that question.

    The term whole number was coined by the mathematics education community denote the set \{0,1,2,\cdots\}. This due to the troubled history of zero. So they call the set \{1,2,\cdots\} the natural numbers.
    In my view, most working mathematicians include 0 in the set of natural numbers due to the fact that we start with 0 being identified with \emptyset.
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    Re: Do you consider zero to be a whole number? Positive or negative?

    And 0 is neither positive nor negative.
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    Re: Do you consider zero to be a whole number? Positive or negative?

    Quote Originally Posted by Plato View Post
    In my view, most working mathematicians include 0 in the set of natural numbers due to the fact that we start with 0 being identified with \emptyset.
    I don't. It's not natural to count "nothing", since you can not see "nothing".
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    Re: Do you consider zero to be a whole number? Positive or negative?

    I have only encountered 0 as a natural number in computer science for instance a language theory class.
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    Re: Do you consider zero to be a whole number? Positive or negative?

    I consider zero to be a whole number but not a natural number. Generally when I am wanting to say that x is a whole number, I say  x \in \left( \mathbb{N} \cup \{0\} \right). My professors and advisor seem to agree with me on this.

    Also, I consider zero to be neither positive nor negative. However, it is an even number.
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    Re: Do you consider zero to be a whole number? Positive or negative?

    Quote Originally Posted by thm43608 View Post
    I consider zero to be a whole number but not a natural number. Generally when I am wanting to say that x is a whole number, I say  x \in \left( \mathbb{N} \cup \{0\} \right). My professors and advisor seem to agree with me on this.
    Several replies have agreed with this point-of-view.
    I would ask to be shown a widely used set theory textbook that does not include zero as a natural number.
    I know of only two minor texts that do not.
    Peano originally began his axioms on natural numbers with 0.
    Hilbert adopted that convention even though Dedekind very much disagreed.
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    Re: Do you consider zero to be a whole number? Positive or negative?

    Ribenboim (1996) states "Let be a set of natural numbers; whenever convenient, it may be assumed that ."

    I think that it probably does not matter too much as long as you define the natural numbers first and use the set consistently.
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