Sign (mathematics)

A sign or signum (from the Latin signum sign ) is a character that is preceded by a real number, in order to be reported as positive or negative. A negative number is always provided with the minus sign, a plus sign may be preceded by optional while a positive number. The number zero is usually considered to be unsigned, but also a signed zero is sometimes in the representation of numbers in the computer used.

Strictly speaking, the mathematical operator for addition ( binary plus) or subtraction (binary minus) and the inversion operator of the addition ( unary minus ) must be the sign that is always unary, can be distinguished. The latter is the sign of a number constants nor the next. However, there are programming languages ​​that know a separate special characters for identification of negative numerical constants, such as APL.

For the sign -related variables, such as rotation angles and directions, there are often different sign conventions.

Plus and minus signs

In arithmetic, the sign of a number is indicated by a leading plus or minus sign. Here, the same numerals are used as for the addition and subtraction of two numbers. The sign is in this case connected with no white space directly to the first digit. For example, designate

Each of the positive and negative number three. If no sign is specified, a number is considered positive. In algebra, the minus sign is used as a unary minus to sign reversal, whereby the respective counter number is obtained. For example,

By the absolute value function, the sign of a negative number is reversed, while a positive number will remain unchanged. For example,

With the Plus or minus a number is in the can have a positive or negative sign.

Sign of the zero

The number zero is neither positive nor negative, and therefore has no sign. The additive inverse of the number zero is called the zero itself thus

The same number of zero. However, the numbers of machines, positive and negative zero are sometimes viewed as two different numbers. Examples are the one's complement integers or IEEE 754 standard for floating point numbers. In some applications, the notation is in use when a negative number is rounded to zero. In calculus, the notation

Used in the formation of a right-sided or left-sided limit.

Sign function

With the help of the sign function or signum function the sign of a (real) number of variables can be determined. The sign function is usually carried

Defined. Accordingly, if the number is positive, and if it is negative. Is, then, the sign function can also use the absolute value function by

Be defined.

Sign conventions

For many sizes directed the assignment of a sign is performed, that is, the values ​​as a positive and which are considered negative in a natural way. In some cases, however, the choice of sign is arbitrary and at most uniformly selected for consistency. In these cases, one speaks of a sign convention.

Sign of angles

A directed angle has, as opposed to an undirected angle, an orientation that is specified on a sign in front of the size of the angle. In particular at an angle of rotation are at the sign, if the rotation is clockwise or counterclockwise. Although this different conventions are used, it is common in mathematics to view counter-clockwise rotations as positive and clockwise rotations as negative.

It is also possible to assign a rotation in three dimensions, a sign, provided that the rotational axis has an orientation. After the right- hand rule rotation is considered an axis oriented counterclockwise in a legal system to be positive and in a left-handed system as negative.

Sign of changes

Changed in size over time, then the change in size is typically defined as

With this convention, corresponds to an increase of a positive change, while a reduction of a negative change corresponds. Analysis of the same convention used in the definition of the derivative. As a result, has a monotonically increasing function differentiable a positive derivative as a monotonically decreasing function having a negative derivative.

Sign of directions

In analytic geometry and physics often certain directions are recognized as positive or negative. As a basic example, the number line is usually drawn with the positive numbers to the right and negative numbers on the left:

Therefore, in the context of uniform motions, displacement or velocity vectors pointing to the right, usually considered positive, while a vector pointing to the left, is considered negative.

In a Cartesian coordinate system, the directions are typically considered to be positive to the right and above, wherein the direction corresponds to the right of the positive x-axis and the upward direction of the positive y-axis. A displacement or velocity vector broken down into its components, then the vertical component of a movement by a positive top and a downward movement will be negative. In geodetic coordinate systems, however, the x and y axis are exchanged.