Talk:Indexed family

message: There seems to be a mistake in the Notation section in the article. It appears to me that it purports to write two notations, a usual and a misleading one, but both notations look the same to me. -- Jitse Niesen 04:14, 15 Jun 2005 (UTC)
thread_title: Notation

message: JA: The lead of the article begins with an informal definition, but not one so casual that it would be refused service at your average fast food restaurant, and so it contains the word "usually" as a sop to diners from computer science who commonly adapt the idea of an indexed set to their notion of a "union datatype".  But that's no reason to sell them the store and get out of the business, if you catch my drift.  Jon Awbrey 12:02, 7 June 2006 (UTC)
replies: text: I don't like the "lookup table" being right at the top, since it's neither a mathematical term nor a familiar common usage term.  I believe it's a computer science term?  -lethe talk [ +] 12:46, 7 June 2006 (UTC)

text: The section Mathematical statement defines a "family of elements" simply as a function. Kreyszig only talks about a "family of elements" being "given by" a map from a nonempty set called the index set into another nonempty set (Kreyszig: Introductory Functional Analysis with Applications, A1.3, p. 617). Likewise he uses the word into when referring to the special case of a sequence. He cautions, "one must be careful to distinguish a family from the subset of X whose elements are the elements of the family" (i.e. from the range of the function). The article at Wolfram Mathworld cites a "formal definition" according to which a family is a map f : I --> X (Bourbaki: Eléments de Mathématiques. Théorie des Ensembles). Again, no requirement for surjectivity is stated in the definition itself; but their equation (6) seems to assume it.Dependent Variable (talk) 06:17, 12 November 2010 (UTC)
thread_title: Definition

message: We can see this kind of statement in too many mathematical texts, but don't know its "formal definition", just because it's an everyday English statement, it's a convention in math, isn't it? Moreover, "a collection of ..." and "a family of ..." are all conventions, not the synonym of set, class, or whatever. When most authors use those statement, I think they don't care what their "formal definition" is. We just need to care only when the axiom of choice exists, and use other terms.--Kilva (talk) 09:45, 10 March 2012 (UTC)
thread_title:  "a family of ... indexed by ..." is just a convention, isn't it? 

message: I noticed that index set and indexed set link to two different articles on Wikipedia. Is this factually correct, or is it an error?  Jarble (talk) 14:52, 27 November 2012 (UTC)
thread_title: Is an "index set" distinct from an "indexed set"?

message: Where does the surjectivity requirement on the function `x` come from? This looks heavily outdated to me -- it's from the same paradigm as the concept that a function is just a set of pairs and thus doesn't know its domain and codomain. Nowadays, the functions \left\{1,2\right\} \to \left\{1,2\right\},\ i \mapsto i and \left\{1,2\right\} \to \mathbb{Z},\ i \mapsto i are considered different, so I believe the same should be true of the families \left(i\right)_{i \in \left\{1,2\right\}} \in \left\{1,2\right\}^{\left\{1,2\right\}} and \left(i\right)_{i \in \left\{1,2\right\}} \in \mathbb{Z}^{\left\{1,2\right\}}. And that means we cannot require `x` to be surjective.  — Preceding unsigned comment added by Darij (talk • contribs) 17:42, 21 September 2018 (UTC)
replies: text: No element in  is allowed to remain un-indexed, i.e., the indexing function is surjective. Purgy (talk) 18:54, 21 September 2018 (UTC)
thread_title: Surjectivity

message: Added simple example to illustrate the difference between indexed family and set, relevant to sequence (-1,1,-1,1,...). Some other things in the article could be cleaned up, but didn't do so. Also, while the concept is completely standard (though not well-referenced), the terminology may be less so. I guess almost all/most/many/quite a few/some... mathematicians don't distinguish between families and sets, but just refer to indexed sets. Reader634 (talk) 11:06, 2 July 2021 (UTC)
thread_title: Edit