1
$\begingroup$

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.)

  • 6
    [Sequence](http://en.wikipedia.org/wiki/Sequence)?2012-08-01
  • 0
    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”.2012-08-01
  • 0
    Looks like that's the right answer. But I can't accept comments, only answers. ;-)2012-08-01

1 Answers 1

3

From Wikipedia entry on sequences:

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.

  • 0
    I thought "sequence" meant the same as "series". But apparently it does not...2012-08-01
  • 0
    It's common confusion. [Series](http://en.wikipedia.org/wiki/Series_(mathematics)#Definition) is the associated sum of a sequence.2012-08-01
  • 0
    Yes, I see that now.2012-08-01
  • 0
    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.2012-08-01
  • 0
    @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.2012-08-03
  • 0
    Yes, why not. If you do not insist on countability ...2012-08-04