21
$\begingroup$

In the set of real numbers, there is no negative zero. However, can you please verify if and why this is so? Is zero inherently "neutral"?

$\endgroup$
5
  • 2
    $\begingroup$ Is there positive zero? Not directly related, but it might be interesting to read this $\endgroup$
    – newbie
    Commented Feb 7, 2014 at 17:15
  • 1
    $\begingroup$ I thought it was more an issue that $+0 = -0 = 0$ rather than $+0$ and $-0$ not existing. $\endgroup$ Commented Feb 7, 2014 at 17:19
  • 6
    $\begingroup$ Yes, with IEEE floating point numbers, but that's a matter for sci comp stackexchange. $\endgroup$
    – abnry
    Commented Feb 7, 2014 at 17:20
  • $\begingroup$ en.wikipedia.org/wiki/Signed_zero $\endgroup$ Commented Jun 15, 2016 at 13:08
  • $\begingroup$ If you're rounding up from a negative number, you can get a negative 0. $\endgroup$ Commented Feb 15, 2021 at 0:10

3 Answers 3

25
$\begingroup$

There is a negative $0$, it just happens to be equal to the normal zero. For each real number $a$, we have a number $-a$ such that $a + (-a)=0$. So for $0$, we have $0+(-0)=0$. However, $0$ also has the property that $0+b=b$ for any $b$. So $-0=0$ be canceling the $0$ on the left hand side.

$\endgroup$
3
  • 9
    $\begingroup$ -1. Zero is neither positive nor negative. The definition of positive (resp. negative) is that $a>0$ ($a<0$), and it's obvious that $0$ satisfies neither. $\endgroup$ Commented Sep 5, 2016 at 13:41
  • $\begingroup$ @YoTengoUnLCD you are rigth. $\endgroup$
    – Jorge B.
    Commented Feb 8, 2017 at 17:00
  • 1
    $\begingroup$ @YoTengoUnLCD When the answer says "negative zero," it is referring to the inverse of zero under addition, not literally a zero that is negative. $\endgroup$ Commented Oct 15, 2020 at 19:18
2
$\begingroup$

My thought on the problem is that all numbers can be substituted for variables. -1 = -x. "-x" is negative one times "x". My thinking is that negative 1 is negative 1 times 1. So in conclusion, I pulled that negative zero (can be expressed by "-a") is negative 1 times 0, or just 0 (-a = -1 * a).

$\endgroup$
2
$\begingroup$

A common definition of negative is "less than zero". In this sense, zero isn't negative (nor positive for a similar reason).

But the opposite of zero is well defined: it is zero. The unary $+$ or $-$ operators can very well be applied to $0$, with no effect.

One can admit that zero has no sign. The $\text{sign}$ function is usually defined to be $-1,0$ or $1$.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged .