Question

What is a sequence?

   What is a sequence?

Calculus: Early Transcendentals

Calculus: Early Transcendentals

Michael Sullivan,… 1st Edition

Chapter 7, Problem 3

Instant Answer

Solved by Expert James Kiss

02/17/2022

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A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Show more…

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What is a sequence?

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Key Concepts

Sequence

A sequence is an ordered collection of elements where the position of each element is significant. In mathematics, the order of the elements matters, which distinguishes sequences from sets, and elements are typically arranged based on a specific rule or pattern.

Indexing

Indexing refers to the assignment of positions or labels (often natural numbers) to the elements of a sequence. This creates a clear association between each element and its location in the order, allowing for precise definitions, manipulations, and analyses of the sequence.

Function Representation

A sequence can be formally described as a function whose domain is the set of natural numbers (or a subset thereof) and whose codomain is the set from which the elements of the sequence are drawn. This perspective facilitates rigorous treatment of sequences in various branches of mathematics, including analysis and algebra.

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