# Does negative zero exist? [closed]

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"?

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

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.

• -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. Commented Sep 5, 2016 at 13:41
• @YoTengoUnLCD you are rigth. Commented Feb 8, 2017 at 17:00
• @YoTengoUnLCD When the answer says "negative zero," it is referring to the inverse of zero under addition, not literally a zero that is negative. Commented Oct 15, 2020 at 19:18

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).

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 $1$.