What is Sign of 0?

[Marc Clifton]

Sander Rossel wrote:

Please stop belittling me.

Dear Mr. Zero (or is it Mrs. Zero, there is some ambiguity here!), I'm sorry, I had no intention of being n-aught-y. In fact, you are very important! Without you, nothing could not be expressed mathematically. You fulfill a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. And besides, you are at least 3756 years old, and in ancient Egypt you were given a designation that means "beautiful", which is much better than what the Babylonian's did, which was to represent you with a space, a blank, a nothing! Of course, the Greeks weren't sure about you -- how could nothing be something! Well, I know that you are something indeed, and certainly, based on your age, much wiser than I. Your humble servant, Marc

Imperative to Functional Programming Succinctly Contributors Wanted for Higher Order Programming Project! Learning to code with python is like learning to swim with those little arm floaties. It gives you undeserved confidence and will eventually drown you. - DangerBunny

[Sander Rossel]

Hah! It was I, Sander Rossel, disguised as 0 all along! You're my servant now :D Or was I 0 disguised as Sander...? Anyway, don't divide by me just in case :~

Read my (free) ebook Object-Oriented Programming in C# Succinctly. Visit my blog at Sander's bits - Writing the code you need. Or read my articles here on CodeProject.

Simplicity is prerequisite for reliability. — Edsger W. Dijkstra

Regards, Sander

[Kiriander]

Quite easy: lim(-1/x,x->INF) makes a negative 0. You have to understand that the limit 0 is an entirely different beast from the 0 you get in your wallet when you spend all your money.

[Daniel Pfeffer]

patbob wrote:

Of course, with IEEE floating point, -0.0 is representable, but allowing it would be inconsistent, and very, very confusing.

Actually, negative zero is essential for correct solution of certain problems involving branch cuts for complex elementary functions. See W. Kahan's Branch Cuts for Complex Elementary Functions, or Much Ado About Nothing's Sign Bit[^]. Note that a reference to the final article is given on Kahan's home page, but I don't have access to that publication.

If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

[benf2]

Typically, one takes the ones compliment and then increment to find the inverse, so that when the numbers added together is "0". So the inverse of 0 is 0. This means that -0 == 0. So, zero has the ability to have both signs.

[Plamen Dragiyski]

Ian Shlasko wrote:

I'd like to know how they represent -0 internally...

That's exactly where is the problem. I don't know C# (I'm currently a javascript programmer), but a Number is internally stored as IEEE754 floating point, which have a bit for sign. It is not an integer. Zero can be represented without the sign bit, therefore when sign bit is 0, you get +0.0, when it is 1, you get -0.0. It is just a bit interpretation problem. If you are interesting why -0.0 work as it is, there is very good mathematical theory for infinitesimals. But as a rule of a thumb, never use == on floating-point number. It returns false more often than you expect to.

[Kirk 10389821]

Actually, I believe the correct answer is Gemini! (I know I married them)

[Ygnaiih]

Damn you people. I started looking into this then I wrote the following: if (-0 == +0) { Console.WriteLine(Math.Sign(0)); } that was C# it returned 0 as expected. Now I am wondering if math is real.

[Member 10267903]

Not only Python. Try it in SQL Server 2012:

declare @A as float;
declare @B as float;
declare @C as float;

set @A = 0.0;
set @B = -1.0;
set @C = @A * @B;

print @C;

or PHP:

$A = -1.0 * 0.0;
echo $A . "\n";

[ormonds]

If 0 represents the contents of my glass then zero is very definitely negative.

[Charles Programmer]

I find 0.0 to be negative when it involves the quantity of money in my control. ;)

[Charles Programmer]

I find 0.0 to be negative when it involves the quantity of money in my control. ;)

[Chris SAS]

Another trick for C#: use the Ceiling function.

static void Main(string[] args)
{
double a = Math.Ceiling(-0.1);
double b = 1 * 0;
double c = -1 * 0;
Console.WriteLine("a = Math.Ceiling(-0.1), a=" + a.ToString());

 byte\[\] bytes;
 bytes = BitConverter.GetBytes(a);
 Console.WriteLine("Bytes of a:");
 Console.WriteLine(BitConverter.ToString(bytes));

 Console.WriteLine("b = 1 \* 0, b=" + b.ToString());
 bytes = BitConverter.GetBytes(b);
 Console.WriteLine("Bytes of b:");
 Console.WriteLine(BitConverter.ToString(bytes));

 Console.WriteLine("c = -1 \* 0, c=" + c.ToString());
 bytes = BitConverter.GetBytes(c);
 Console.WriteLine("Bytes of c:");
 Console.WriteLine(BitConverter.ToString(bytes));

}

Output:

a = Math.Ceiling(-0.1), a=0
Bytes of a:
00-00-00-00-00-00-00-80
b = 1 * 0, b=0
Bytes of b:
00-00-00-00-00-00-00-00
c = -1 * 0, c=0
Bytes of c:
00-00-00-00-00-00-00-00

I wrote about this some years ago for our SAS programming users (What's the difference between 0 and -0?[^]), as a similar IEEE 754 behavior exists there.

[Matt T Heffron]

The flaw in this is that b and c are both calculated as integer values (at compile time) then converted to double. Integer doesn't have a negative zero.

"Fairy tales do not tell children the dragons exist. Children already know that dragons exist. Fairy tales tell children the dragons can be killed." - G.K. Chesterton