This essay focuses on times at different positions.n the instructions there are some questions, please do the book review according to that. 4. please read the whole book.

times at different positions

1. the instructions are in the form of pictures that I attached in the files, in the name sequence as book. Please use book chapters as references, do not use another outside source. 3. In the instructions there are some questions, please do the book review according to that. 4. please read the whole book.

In mathematics, a sequence is an enumerate collection of objects in which repetitions are allow and order matters.

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, the same elements can appear multiple times at different positions in a sequence. And unlike a set, the order does matter. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences). The set of the first n natural numbers (for a sequence of finite length n).

For example, (M, A, R, Y) is a sequence of letters with the letter ‘M’ first and ‘Y’ last. This sequence differs from (A, R, M, Y). Also, the sequence, which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers.

The position of an element is the natural number for which the element is the image.

The first element has index 0 or 1, depending on the context or a specific convention. In mathematical analysis, a sequence is often denoted by letters. In the form of  where the subscript n refers to the nth element of the sequence. For example, the nth element of the Fibonacci sequence .  Generally denote.

In computing and computer science, finite sequences are sometimes call strings. Words or lists, the different names commonly corresponding to different ways to represent them in computer memory. Infinite sequences are called streams. The empty sequence ( ) is included in most notions of sequence, but may be exclude depending on the context.