Negative number

Add positive and negative numbers, the real numbers without the zero ( ) can be distinguished in mathematics. A number which is greater than zero, such as three, it is called a positive; If it is less than zero, such as -3 they are called negative. Positive numbers carry a plus sign ( ) and negative numbers with a minus sign (-) as the sign. The plus sign is usually omitted when recording the number. The number zero as a value neither positive nor negative.

The same distinction can be made in subsets of real numbers, such as in the rational numbers or integers.

Since you can not define acceptable order for some sets of numbers (eg complex numbers) with the addition and multiplication, one can not speak of greater or less than zero for these numbers also. For the exact requirements of such order relation see ordered field.

Representation

Positive numbers are unsigned or marked with a plus sign, negative numbers with a minus sign. The sign is connected with no white space directly on the first digit. Especially in the financial sector negative numbers alternatively be written in parentheses.

On the number line, the range of positive numbers is mirror symmetric to the region of negative numbers. The distance a figure A 0 is equal to the distance of 0 to the number of -A, and is called the amount of the number.

Properties

Sign

The sign has a number of positive or negative. The sign function returns depending on the sign of an integer value -1 for negative numbers, 0 for 0, and 1 for positive numbers.

Counter number

The number a is called the counter number to a; A number is reversed from A to. 0 is its own additive inverse.

Amount

The value of a number is equal to the distance of the number to the number 0, the sum of a number a is equal to the amount of its additive inverse -a.

Natural Numbers

The term " positive " or " negative value " can be transferred to a whole number ( embedded in the real numbers ). The natural numbers are the positive (or with the appropriate definition of the non-negative ) integers. Here, the notation ( positive integers only ) or ( non-negative integers ) has naturalized.

Multiplicative group of

Summing up the positive real (or rational ) numbers to the set P together and the negative real (or rational ) numbers for the amount of N, so is the union of the sets P and N, ie the set of all non-zero numbers, an Abelian group with respect to multiplication.

For example, since the integer 2 ( with respect to multiplication ) no inverse integer is (1/2 is not an integer ), this does not apply to whole numbers.

Minus times minus equal Plus

If you multiply two negative or two positive numbers together, you always get a positive number. Multiplying the other hand, a positive to a negative number, the result is always negative.

Sign Error

Many calculation errors based on a confusion of the sign.

A well-known example is the high bridge over the Rhine, where it was used in the bridge pier calculating the correction value of 27 cm with the wrong sign. Switzerland and Germany have different by 27 cm height system.

Practical Uses

In some areas, special terms have been established by the use of negative numbers is avoided. Thus one speaks, for example, by debt instead of negative credit or brakes instead of negative acceleration. On the other hand scales have been established with positive and negative numbers in some places, where negative numbers would not be necessary, such as when measuring temperature (Celsius and Fahrenheit scale instead of the Kelvin scale).