Codomain

In the context of a mathematical function, which maps elements of a set of elements of a set is called a target amount or range of values ​​of the function.

For the word set of values ​​or range of values ​​is frequently used; but these words often refer to the picture instead of quantity. So there is likelihood of confusion. In Germany there is clarity in the classroom, it is only the identifier of values ​​( range of values) used in the sense of image set. The target amount is only the stock of possible values ​​of - it's not mandatory that they are actually adopted by all.

The amount of the values ​​that appear as a function of a value, the image set. If the image amount equal to the target amount of so called surjective.

The target amount is a distinctive part of a function. Functions with the same domain and the same function rule, but different target amount can never be the same.

Example

The function assigns to each point of the Euclidean plane to its distance from the zero point. Thus:

The target quantity of the function is the set of real numbers. Since the distance can never be negative, not all possible values ​​are adopted. The image set consists exactly of the non-negative real numbers (often referred to ).

The function has the same domain, the same function rule and the same image set as. However, since the target sets are different, yet valid.

Relationship between the amounts

Based on the adjacent simple example function should once again the various quantities occurring are explained:

• The definition set ( ) contains the elements 1, 2, 3, 4
• The target quantity () contains the elements a, b ​​, c, d
• The image set consisting of the elements B, C, D. As these three are used as function values ​​.
• Domain is another word for definition of quantity.
• Range of values ​​is another word for target quantity.
• Set of values ​​and range of values ​​are not clearly defined in their meaning and can the target amount, or else the image set, respectively. In Germany there is clarity in the classroom, it is only the identifier of values ​​( range of values) used in the sense of image set.