# Generalities.

Definition 2.1.1   Let and be two sets. An application (or a mapping) from to is defined by a subset such that . We denote .

Notation:

Given an application : the domain of and the range of .

Remark 2.1.2   Two applications and are equal if, and only if, they have the same domain , the same range and .

Definition 2.1.3   Let be three sets and and be two applications. The composition of with is the application such that .

Example 2.1.4   Let and are given by and , then:

Example 2.1.5   The function given by is equal to , where:
• ;
• .

Remark 2.1.6   Generally , even when both compositions are well-defined.

With the settings of Example 1.4:

Thus , according to remark 1.2.

Noah Dana-Picard 2007-12-28