Nombor negatif dan nombor bukan negatif

Sesuatu **nombor negatif** merupakan suatu nombor yang lebih kurang daripada 0, seperti −3.  Sesuatu **nombor positif** merupakan suatu nombor yang lebih besar daripada 0, seperti 3.  0 sendiri bukan negatif mahupun positif.  **Nombor-nombor bukan negatif** merupakan nombor nyata yang bukan negatif (sama ada positif atau kosong). **Nombor-nombor bukan positif** merupakan nombor yang bukan positif (sama ada negatif atau kosong).

Dalam konteks nombor kompleks, *positif* adalah *nyata*, tetapi demi kejelasan seseorang juga boleh sebut "nombor nyata positif".

## Fungsi signum
Adalah mungkin untuk menentukan sesuatu fungsi sgn(*x*) pada nombor nyata yang adalah 1 bagi nombor positif, −1 bagi nombor negatif, dan 0 bagi kosong (kadangkala digelar fungsi signum):
:\sgn(x)=\left\{\begin{matrix} -1 & : x  0 \end{matrix}\right. 

Dengan ini kita ada (kecuali bagi *x*=0):
:\sgn(x) = \frac{x} = \frac{x} = \frac{d}{d{x}} = 2H(x)-1. 
Di mana |*x*| merupakan nilai mutlak untuk *x* dan *H*(*x*) merupakan Heaviside step function. Lihat juga terbitan (matematik).

## Fungsi Signum kompleks
It is possible to define a function csgn(*x*) on the complex numbers which is 1 for positive numbers, −1 for negative numbers and 0 for zero (sometimes called the complex signum function):
:\operatorname{csgn}(x)=\left\{\begin{matrix} -1 & : x  0 \end{matrix}\right. 

Where the complex inequality should be interpreted as follows
:
\begin{cases}
 x>0 \iff \operatorname{Re}(x) > 0 \vee (\operatorname{Re}(x) = 0 \land \operatorname{Im}(x) > 0) \\
 x

We then have (except for *x*=0):
:\operatorname{csgn}(x) = \frac{x}{\sqrt{x^2}} = \frac{\sqrt{x^2}}{x} = \frac{d{\sqrt{x^2}}}{d{x}} = 2H(x)-1. 

## Lihat juga

* Nombor hipernyata
* Integer
* Rational number
* Nombor nyata
* Surreal number
* −0
* Sejarah matematik


## Catatan dan rujukan
* Maseres, Francis, 1731–1824. *A dissertation on the use of the negative sign in algebra: containing a demonstration of the rules usually given concerning it; and shewing how quadratic and cubic equations may be explained, without the consideration of negative roots. To which is added, as an appendix, Mr. Machin's Quadrature of the Circle*, 1758. Quoting from Maseres' work, "If any single quantity is marked either with the sign + or the sign − without affecting some other quantity, the mark will have no meaning or significance, thus if it be said that the square of −5, or the product of −5 into −5, is equal to +25, such an assertion must either signify no more than 5 times 5 is equal to 25 without any regard for the signs, or it must be mere nonsense or unintelligible jargon."
* Colva Roney-Dougal, Lecturer in Pure Mathematics at the University of St Andrews, stated this on the BBC Radio 4 "In Our Time", on Negative Numbers, 9 March 2006.
* *Knowledge Transfer and Perceptions of the Passage of Time*, ICEE-2002 Keynote Address by Colin Adamson-Macedo. "*Referring again to Brahmagupta's great work, all the necessary rules for algebra, including the 'rule of signs', were stipulated, but in a form which used the language and imagery of commerce and the market place. Thus 'dhana' (= fortunes) is used to represent positive numbers, whereas 'rina' (= debts) were negative*". http://www.ineer.org/Events/ICEE2002Info/Adamson-MacedoKeynotePaper.pdf
* Alberto A. Martinez, *Negative Math: How Mathematical Rules Can Be Positively Bent*, Princeton University Press, 2006; a history of controversies on negative numbers, mainly from the 1600s until the early 1900s.


## Pautan luar
*BBC Radio 4 series "In Our Time", on ''Negative Numbers'', March 9, 2006 
*Endless Examples & Exercises: ''Operations With Signed Integers''

*VERY intersting and insightful concept of negative numbers