Definition:Finite Sequence

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 $n \in \N$

• Definition:Infinite Sequence

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

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