# Talk:Index set

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## Phrasing

In mathematics, an index set I is another name for a function domain.

This statement seems to me to exemplify a deficiency in the way mathematicians think. Currently accepted canons of logical rigor will bless this assertion, but nonetheless mathematicians are thinking about something differently when they call it an index set than when they call it a domain of a function. Everyone can explain the difference if they think about it, but only when speaking "informally". Michael Hardy 20:32, 15 Dec 2003 (UTC)

Hardly 'brilliant prose', I'd agree. And just the same point as could be made about sequence, I guess. I'd deny it is a problem with thinking, though.

Charles Matthews 21:09, 15 Dec 2003 (UTC)

I think there is a difference, and it is inappropriate to call any index set a function domain, because IMHO, not any family is a function. Families can have their elements in categories (see coproduct) or still elsewhere, where a union does not make sense, IMHO. MFH 00:37, 10 Mar 2005 (UTC)

I agree with Hardy that defining an index set as a function domain, while technically correct, is very unilluminating. I tried to rewrite this article so that it makes more sense. -- Fropuff 18:14, 2005 May 26 (UTC)

I couldn't figure out what an index set was until I read the statement above; it really solidified it for me. Though, I'm no mathematician. I do think the statement could help those of us who don't already know set theory, even if the statement isn't entirely true. -- Toper

## Using {Ai} for families

A family and the set of all elements of the family are certainly distinct. The first one is ordered (at least if the index set is ordered) and the second one is not. So I don't think it's a good idea to use the same notation for both.

Ai is the i-th element, {Ai | i∈I} is the unordered set of elements and (Ai)iI is the ordered family.

Though I have seen lots of books using {Ai} for a family it's confusing and unnecessary.

Furthermore the title and the disambiguation page are misleading, this page is mainly not about the index set but about the indexed set or family. Markus Schmaus -- 21:56 3 Jun 2005 (UTC)

## confusion

In the notation (Ai), the symbol A is the mapping, and not the codomain of the mapping. I'll change the article. Bo Jacoby 08:44, 7 June 2006 (UTC)

## typo?

In the first example, should it be "${\displaystyle f:J\rightarrow S}$ is the particular enumeration of S" instead?

## Merger Proposal

• Oppose This is self contained section and contains useful information. So, not a good idea to merge them. Phoe6 (talk) 23:38, 25 April 2011 (UTC)

Here is problem with part denoted "indicator function", such that function here described corresonds to comparing of two elements in the set, but this function does not says anything abou appearance of some element of set in the (some) its subset in any case. Please fix this ambiguity — Preceding unsigned comment added by Jiri 1984 (talkcontribs) 19:36, 11 October 2011 (UTC)

## Is an "index set" the same as an "indexed set", or is this an error?

I noticed that index set and indexed set link to different articles on Wikipedia. Is this correct, or is it an error? Jarble (talk) 14:55, 27 November 2012 (UTC)

No, it's not an error. It's like the difference between a lessor and a lessee: they're at opposite ends of a relationship. — Quondum 15:16, 27 November 2012 (UTC)