# Talk:Sequence

WikiProject Mathematics (Rated C-class, Top-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 C Class
 Top Importance
Field: Basics
One of the 500 most frequently viewed mathematics articles.

## braces or parentheses?

I came to this article looking for some confirmation that a convention I have always used is a "standard" convention:

braces {M,A,R,Y} are used to denote (unordered) sets

parentheses (M,A,R,Y) are used to denote (ordered) sequences

I notice that the article uses braces for sequences. I am still unsure this is "standard" so I won't edit... but thought I should raise it

Agneau (talk) 15:05, 14 February 2013 (UTC)

In some contexts, where unordered sets are rare, braces are sometimes used for sequences. I believe you are correct, except that $\{a_n\}_1^\infty$ is often used instead of $(a_n)_1^\infty$ as a compact notation for sequences, and sometimes a different symbol is used for multi-sets. I would bring it up on WT:MATH, but I would have no objection to changing most of the braces to parentheses. — Arthur Rubin (talk) 15:20, 14 February 2013 (UTC)
• As far as I know, this article used round brackets for sequences up until #Did an extensive revision mentioned above, so there may be consensus to go back. Also, I suspect using different notations would help distinguish sets and alphabets from sequences. Vadmium (talk, contribs) 23:46, 14 February 2013 (UTC).
• Just looking in books within reach... Serge Lang uses braces in his Analysis. Briggs and Cochran (boo) also use braces. Having done nothing but set theory lately, I felt sequences should look like $\left(a, b, \ldots\right)$ or $\langle{}a, b, \ldots\rangle{}$, but I guess it's not an issue in fields that don't talk a lot about ZF sets. melikamp (talk) 03:56, 8 March 2013 (UTC)

OK, just now I changed the braces back to parentheses. Actually, angle brackets might be the most suitable of all for my taste and experience, which is limited but not too limited. But this way is fine too. I'll leave them as parentheses because they were that way before December 20, 2012. --Hoziron (talk) 02:36, 16 April 2013 (UTC)

Looks good. I believe this notational issue should be part of the article. I would bring it up in the first section, perhaps the second paragraph. If there are no objections I will change insert it myself. Brent Perreault (talk) 21:57, 3 September 2013 (UTC)
Please do. But don't forget to mention that frequently no brackets of any sort are used. Perhaps the most common notation for a sequence is just a list with commas: a, b, c, ... . McKay (talk) 05:20, 4 September 2013 (UTC)

## Limit of a sequence

Why does this article only define convergence of a sequence in a metric space, rather than a general topological space? I know there's a link to "Limit of a sequence," but at the very least this page should give the reader some indication that there's a major concept missing here, and that they need to follow that link to see it. — Preceding unsigned comment added by 165.123.213.202 (talk) 08:09, 10 December 2013 (UTC)

I agree on this. Martinkunev (talk) 19:20, 27 January 2014 (UTC)

## Define "list"

This article gets off to a curious start by saying "A sequence is an ordered list", and list is a disambiguation page. What exactly is the definition of "list" in a mathematical context? Horatio (talk) 01:06, 3 May 2014 (UTC)

Maybe it's just used as an English word, and not a technical term? In that case, it should be unlinked, so that the reader isn't tempted to follow it to the disambiguation page. Horatio (talk) 01:14, 3 May 2014 (UTC)

I guess I'll unlink it. By all means relink it to an appropriate technical article, if relevant. Horatio (talk) 22:43, 4 May 2014 (UTC)

A list is a collection of objects whose orders are important(unlike set and multiset) and repetitions are allowed(unlike set). Therefore the word "ordered" in "ordered list" is redundant. It should be just "list". Any objections? LoMaPh (talk) 00:54, 22 February 2015 (UTC)

Your definition is common among computer scientists, but (unlike that of a mathematical set) hardly known to any other people. Therefore, while your redundancy argument is right, "..., a sequence is a list" doesn't explain anything at all to most people. But what about "..., a sequence, a.k.a. list, is a collection of objects whose orders are important and repetitions are allowed." Would that be ok? - Jochen Burghardt (talk) 06:29, 22 February 2015 (UTC)

Sounds good. LoMaPh (talk) 02:03, 25 February 2015 (UTC)

Why do you say "... whose orders are important ..." rather than "whose order is important"? Mathyeti (talk) 17:05, 12 April 2015 (UTC)

You are right. - If there are no objections to the accordingly corrected version, I'd insert it in the article's lead. - Jochen Burghardt (talk) 19:52, 12 April 2015 (UTC)
Attempting to perform the insertion, I found that D.Lazard did it already on 25 Feb. - Jochen Burghardt (talk) 22:00, 15 April 2015 (UTC)
Thanks all, the current version is much better. Horatio (talk) 01:56, 31 July 2015 (UTC)

## (one-sided)

There are three occurrences of the phrase "(one-sided) sequences", beginning with the section "Definition of convergence". Please define the term. (reader whose mathematical level doesn't quite reach that of the writers) Mathyeti (talk) 17:02, 12 April 2015 (UTC)

Probably, it is used to distinguish from doubly infinite lists, introduced in section Sequence#Finite and infinite. I suggest to introduce the term there. - Jochen Burghardt (talk) 19:52, 12 April 2015 (UTC)
I copy-edited that section, to define the notion of one-sidedness explicitly. - Jochen Burghardt (talk) 21:58, 15 April 2015 (UTC)

## Definition of sequence

Hi, I am changing the definition of "sequence" in the article and I want to describe my motivation. First of all, the original text said that a sequence is "usually defined" as a function whose domain is a countable totally ordered set, but no references are given for this. I would be surprised if any exist, since this is a very strange definition of a sequence. This leads me to my second point, which is that this definition includes as sequences functions whose domains are the set of rational numbers or similarly crazy countable sets. In standard mathematical practice these are not usually considered sequences.

Now I think I understand the motivation behind the previous definition of sequences, which was to allow finite and bi-infinite sequences to be counted as sequences. I've come up with a new definition that includes these as sequences while excluding things like functions whose domain is the rationals. I've also reworded to make it clear that this is not a standard definition, just a convenient one.

I've also reworded the citations to avoid giving the impression that there is broad consensus on how to define a sequence within any given field. As far as I know this is not true, although I would guess that the most common definition (in all fields) is that a sequence is any function whose domain is N.

David9550 (talk) 15:33, 21 January 2016 (UTC)