# Name for a set which has an order?

As we all know, a set is a collection of elements which have no particular order and no multiplicity.

So what do you call a construct which does store its elements in a specific order? What is the correct mathematical term for that?

(I looked at "ordered set", but that apparently means something quite different - it is a set who's elements support order comparisons.)

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–  user2468 Aug 1 '12 at 13:54
And if @J.D.'s guess is wrong, you'll have to tell us what, precisely, you mean by the phrase “store its elements in a specific order”. –  Harald Hanche-Olsen Aug 1 '12 at 14:05
Looks like that's the right answer. But I can't accept comments, only answers. ;-) –  MathematicalOrchid Aug 1 '12 at 14:12

## 1 Answer

In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms), and the number of ordered element (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence.

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I thought "sequence" meant the same as "series". But apparently it does not... –  MathematicalOrchid Aug 1 '12 at 14:15
It's common confusion. Series is the associated sum of a sequence. –  user2468 Aug 1 '12 at 14:19
Yes, I see that now. –  MathematicalOrchid Aug 1 '12 at 14:30
Since this is MATH.stackexchange: a sequence is a surjective map $I\rightarrow X$, where $I$ is a totally(?) ordered set. The elements of $X$ are the members of the sequence. So a sequence is a particular case of an indexed set. –  Hagen Knaf Aug 1 '12 at 14:36
@Hagen: So the identity on $\mathbb R$ is also a sequence? After all, it is a surjective map $I\to X$ (where both $I$ and $X$ are $\mathbb R$), and $I$ (that is, $\mathbb R$) is totally ordered. –  celtschk Aug 3 '12 at 18:42