History of Sequence

	Revision 7 . . (edit) October 12, 2001 3:08 am by AxelBoldt
	Revision 6 . . (edit) October 12, 2001 2:40 am by Zundark [fix a link]
	Revision 5 . . September 4, 2001 3:14 am by Zundark [fix definition, after someone changed it without regard to the rest of the article]
	Revision 4 . . August 31, 2001 9:02 am by (logged).148.162.xxx

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Difference (from prior major revision) (minor diff, author diff)

Changed: 1c1

In mathematics, a sequence is a list, often infinite, x1, x2, x3, ...

In mathematics, a sequence is an infinite list x1, x2, x3, ... (Sometimes finite lists are also called sequences, but not in the mathematical part of this article.)

Changed: 5c5

If S is the set of integers, then the sequence is an [integer sequence]?.

If S is the set of integers, then the sequence is an integer sequence.

Changed: 7c7

If S is endowed with a topology then it is possible to talk about convergence of the sequence. A sequence converges to a limit x if every open set containing x also contains all but finitely many of the terms of the sequence. For example, the sequence of real numbers 1/2, 1/3, 1/4, 1/5, ... converges to 0. In general, it is possible for a sequence to converge to more than one limit, but this cannot happen in a Hausdorff space. A sequence that does not converge to any point is said to diverge.

If S is endowed with a topology then it is possible to talk about convergence of the sequence. A sequence converges to a limit x if every open set containing x also contains all but finitely many of the terms of the sequence. For example, the sequence of real numbers 1/2, 1/3, 1/4, 1/5, ... converges to 0. In general, it is possible for a sequence to converge to more than one limit, but this cannot happen in a Hausdorff space. A sequence that does not converge to any point is said to diverge.

Added: 34a35