<P> In mathematics , a sequence is an enumerated collection of objects in which repetitions are allowed . Like a set , it contains members ( also called elements , or terms ) . The number of elements ( possibly infinite ) is called the length of the sequence . Unlike a set , order matters , and exactly the same elements can appear multiple times at different positions in the sequence . Formally , a sequence can be defined as a function whose domain is either the set of the natural numbers ( for infinite sequences ) or the set of the first n natural numbers ( for a sequence of finite length n ) . The position of an element in a sequence is its rank or index ; it is the integer from which the element is the image . It depends on the context or of a specific convention , if the first element has index 0 or 1 . When a symbol has been chosen for denoting a sequence , the nth element of the sequence is denoted by this symbol with n as subscript ; for example , the nth element of the Fibonacci sequence is generally denoted F . </P>
<P> In mathematics , a sequence is an enumerated collection of objects in which repetitions are allowed . Like a set , it contains members ( also called elements , or terms ) . The number of elements ( possibly infinite ) is called the length of the sequence . Unlike a set , order matters , and exactly the same elements can appear multiple times at different positions in the sequence . Formally , a sequence can be defined as a function whose domain is either the set of the natural numbers ( for infinite sequences ) or the set of the first n natural numbers ( for a sequence of finite length n ) . The position of an element in a sequence is its rank or index ; it is the integer from which the element is the image . It depends on the context or of a specific convention , if the first element has index 0 or 1 . When a symbol has been chosen for denoting a sequence , the nth element of the sequence is denoted by this symbol with n as subscript ; for example , the nth element of the Fibonacci sequence is generally denoted F . </P>
when is a list of numbers called a sequence
when is a list of numbers called a sequence
a function whose domain is either the set of the natural numbers ( for infinite sequences ) or the set of the first n natural numbers ( for a sequence of finite length n )
a function whose domain is either the set of the natural numbers ( for infinite sequences ) or the set of the first n natural numbers ( for a sequence of finite length n )