# finite sequence

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Related to finite sequence: finite series, Geometric sequence, Infinite sequence

## finite sequence

[¦fī‚nīt ′sē·kwəns]
(mathematics)
A listing of some finite number, n, of mathematical entities that is indexed by the first n positive integers, 1,2,…, n.
More precisely, a function whose domain is the first n positive integers.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
(1) F is said to be of strongly bounded variation (BV) on E if the number [mathematical expression not reproducible] is finite, where the supremum is taken over all finite sequences {[[c.sub.i], [d.sub.i]] of nonoverlapping intervals that have endpoints in E.
It is conjectured every n [member of] <Z [union] I> using the modified form of Collatz conjecture has a finite sequence which terminates at one and only element from the set A or B according as (3a + 1) + (3b + 1)I formula is used or (3a - 1) + (3b -1)I formula is used respectively.
If A [subset or equal to] M, then x [member of] M is definable from A iff there exist an L-formula [phi](v, [??]) and a finite sequence [??] [subset or equal to] A such that x is the unique element v of M with M |= [phi](v, [??]).
Being given two finite sequences x = ([x.sub.0], [x.sub.1],..., [x.sub.N-1]) and y = ([y.sub.0], [y.sub.1],..., [y.sub.N-1]) of the same of the same length N, is called discrete circular convolution of period N the sequence z = x [cross product] y = ([z.sub.0], [z.sub.1],..., [z.sub.N-1]), where
(f) As in (d), [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for every finite sequence ([c.sub.k]).
(1) Here the author shows how things change if you are allowed the option to quit early: Subject to some mild conditions, you should essentially always accept a sufficiently long finite sequence of good bets.
We describe state transitions as follows: We use the notation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to denote that the finite sequence of actions [Beta]' takes the system from state [N, L] to state [N', L'].
No finite sequence of Yablo sentences is paradoxical.
Informally, the difference between a task and a super-task is that a task consists of a finite sequence of actions, while a super-task consists of an infinite sequence of actions.
Observe that the positions of the multiples of 7 can be obtained by successively adding the elements of the finite sequence 12,7,4,7,4,7,12,3.
In the other case, where [beta] < [[alpha].sup.-], from ([P.sub.3] : [[alpha].sup.-]), there exists a finite sequence ([[gamma].sub.0], ..., [[gamma].sub.n]) [member of] [[OMEGA].sup.n+1] satisfying

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