In high school, we have learned the representation of sequence, subsequence and sequence and the boundedness of the sequence . For the convenience of application, it is briefly summarized as follows.

　　Definition 1: Infinite numbers arranged in a certain order

It is called an infinite sequence, or sequence for short , and is abbreviated as .  Each number in the sequence is called a term of the sequence, is called a general term or general term , and is called the subscript of .

figure 1

　　Definition 2: Extract infinite items arbitrarily from the sequence , and maintain the order of these items in the original sequence . The sequence obtained by this extraction method is called a subsequence( or subsequence) of the original sequence.

　　A sequence can be regarded as a moving point on the number axis , which takes values sequentially on the number axis.

,

It can also be viewed as a function whose independent variable is a positive integer :

,

Its domain of definition is the set of all positive integers：. When the independent variable takes in turn , the corresponding function values are arranged in the sequence ( see Figure 2 ) .　　　

figure 2