Non User
Index: > A B C D E F G H I J K L M N O P Q R S T U V W X Y Z	Business Non User Industries Finance Tax

Home > Negative and non-negative numbers

In the context of complex numbers positive implies real, but for clarity one may say "positive real number".

1 Negative numbers

Negative integers can be regarded as an extension of the natural numbers, such that the equation x − y = z has a meaningful solution for all values of x and y. The other sets of numbers are then derived as progressively more elaborate extensions and generalizations from the integers.

Negative numbers are useful to describe values on a scale that goes below zero, such as temperature, and also in bookkeeping where they can be used to represent debts. In bookkeeping, debts are often represented by red numbers, or a number in parentheses.

2 Non-negative numbers

A number is nonnegative if and only if it is greater than or equal to zero, i.e. positive or zero. Thus the nonnegative integers are all the integers from zero on upwards, and the nonnegative reals are all the real numbers from zero on upwards.

A real matrix A is called nonnegative if every entry of A is nonnegative.

A real matrix A is called totally nonnegative by matrix theorists or totally positive by computer scientists if the determinant of every square submatrix of A is nonnegative.

3 Sign function

It is possible to define a function sgn(x) on the real numbers which is 1 for positive numbers, −1 for negative numbers and 0 for zero (sometimes called the signum function):

We then have (except for x=0):

where |x| is the absolute value of x and H(x) is the Heaviside step functionThe Heaviside step function named in honor of Oliver Heaviside, is a discontinuous function whose value is zero for negative inputs and one elsewhere: : The function is used in the mathematics of signal processing to represent a signal that switches on at.

4 Arithmetic involving signed numbers

4.1 Addition and subtraction

For purposes of addition and subtraction, one can think of negative numbers as debts.

Adding a negative number is the same as subtracting the corresponding positive number:

(if you have $5 and acquire a debt of $3, then you have a net worth of $2)

Subtracting a positive number from a smaller positive number yields a negative result:

(if you have $4 and spend $6 then you have a debt of $2).

Subtracting a positive number from any negative number yields a negative result:

(if you have a debt of $3 and spend another $6, you have a debt of $9).

Subtracting a negative is equivalent to adding the corresponding positive:

(if you have a net worth of $5 and you get rid of a debt of $2, then your new net worth is $7).

Also:

(if you have a debt of $8 and get rid of a debt of $3, then you still have a debt of $5).

4.2 Multiplication

Multiplication of two negative numbers yields a positive result: (−3) × (−4) = 12. This situation cannot be understood as repeated addition, and the analogy to debts doesn't help either. The ultimate reason for this rule is that we want the distributive lawIn mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra. For example: : 4 · (2 + 3) (4 · 2) + (4 · 3) In the left-hand side of the above equatio to work:

The left hand side of this equation equals 0 × (−4) = 0. The right hand side is a sum of −12 + (−3) × (−4); for the two to be equal, we need (−3) × (−4) = 12.

Politics	Business	Finance

Topics: Negative And Non-negative Numbers Number Positive Debt Integers...

---

Non-cognitivismNon-cognitivism is the meta-ethical view that ethical statements (such as 'Killing is wrong') are not propositions; that is to say, they do not express factual claims or beliefs and therefore are neither true nor false (they are not truth-apt . This disti NonexistenceNonexistence is sometimes mentioned in discussions of the meaning, or analyzability, of " existence. It is frequently pointed out on this topic that there are a variety of senses in which something can fail to exist (see the following list, as just an exa Non-alcoholic beerNon-alcoholic beer (NAB) is a slightly misleading term used to describe beer with very low alcohol content. The vast majority of NABs are lagers, but there are to a lesser extent some ales. The general opinion of them with regard to taste is not high, wit Non-player characterA non-player character is a fictional character in a role-playing game that is generally used and created by the gamemaster. Non-player characters (or "NPCs") run the gamut — from the Friendly Innkeeper in Dungeons & Dragons to a Fixer or Netrunner in a c Non-standard analysisModel theory In the most restricted sense, nonstandard analysis or non-standard analysis is that branch of mathematics that formulates analysis using a rigorous notion of infinitesimal, where an element of an ordered field F is infinitesimal if and only i Nonlinear opticsNonlinear optics is the branch of optics that describes the behaviour of light in nonlinear media that is, media in which the polarization P responds nonlinearly to the electric field E of the light. This nonlinearity is typically only observed at very hi Non-deterministic Turing machine Non-disclosure agreement Non-steroidal anti-inflammatory drug Non-American casualties of the September 11, 2001 Attacks Non-Aligned Movement Nonjudicial punishment Non-Uniform Memory Access Non-fixed access Non-return-to-zero