# Definition:Finite Sequence

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## Definition

A **finite sequence** is a sequence whose domain is finite.

### Length of Sequence

The **length** of a finite sequence is the number of terms it contains, or equivalently, the cardinality of its domain.

#### Sequence of $n$ Terms

A **sequence of $n$ terms** is a (finite) sequence whose length is $n$.

## Also known as

Some sources use the term **word** in place of **finite sequence**.

Compare the definition of word in the context of formal systems.

Some treatments, in order to stress the difference between a **finite sequence** and infinite sequence, present this term as **finite-sequence**.

## Also see

- Definition:Ordered Tuple: a
**finite sequence**whose domain is specifically $\set {1, 2, \ldots, n}$ for some $n \in \N$

## Sources

- 1958: J.A. Green:
*Sequences and Series*... (previous) ... (next): Chapter $1$: Sequences: $1$. Infinite Sequences - 1960: Paul R. Halmos:
*Naive Set Theory*... (previous) ... (next): $\S 11$: Numbers - 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 18$: Induced $N$-ary Operations - 1971: Robert H. Kasriel:
*Undergraduate Topology*... (previous) ... (next): $\S 1.15$: Sequences: Definition $15.2$ - 1993: Keith Devlin:
*The Joy of Sets: Fundamentals of Contemporary Set Theory*(2nd ed.) ... (previous) ... (next): $\S 1$: Naive Set Theory: $\S 1.7$: Well-Orderings and Ordinals - 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 8$ Definition by finite recursion

- 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (previous) ... (next): Appendix $\text{A}.3$: Definition $\text{A}.12$