Talk:Sufficient Conditions for Basis of Finite Dimensional Vector Space

The current name is just the definition of basis, and it is not transparent. I've been trying to find a good name, but I haven't found anything satisfying. Something like Basis of Finite Dimensional Vector Space or Characterization of Basis of Finite Dimensional Vector Space? I'm not sure. --barto (talk) 05:53, 29 July 2017 (EDT)


 * Definition:Basis of Finite Dimensional Vector Space works for me, with three subpages: /Definition 1, etc.


 * This was an early page written before the structure of the site had properly taken shape. I started to go through and revisit the source work it came from but I got bogged down on the axiomatic definition of the number fields and never got round to continuing with it. --prime mover (talk) 06:48, 29 July 2017 (EDT)


 * I don't think we should define a basis as a generating or linearly independent set, for two reasons:
 * It will confuse students who just learned about those 3 definitions.
 * The proof of this equivalence relies on some results that use a specific definition of a basis, such as Vector Space has Basis Between Linearly Independent Set and Finite Spanning Set.
 * It would mean that those results have to be included in the page that shows the equivalence of the definitions. I'd rather not hide these essential arguments in a definition equivalence page, and overload it with that. Not to mention that some of those results have multiple proofs. It would be a mess.
 * Even in the unlikely case that there is a source that defines a basis as such, the better thing to do is to add a remark at Definition:Basis of Vector Space, linking to this page. --barto (talk) 07:03, 29 July 2017 (EDT)


 * Oh, it didn't actually look like an old page :) It fits miraculously well into the modern structure. I checked Warner (the source of this) and there it's a theorem, after the definition of Basis and Dimension. --barto (talk) 07:09, 29 July 2017 (EDT)


 * That's because this page was taken directly from my own tattered old falling-apart held-together-with-sellotape copy of Warner, and the whole structure of this section of was modelled directly on the expository style of Warner in the first place.


 * I confess I'm not sure I understand what was behind your initial question in the first place, sorry. --prime mover (talk) 08:03, 29 July 2017 (EDT)


 * I just want a title that describes what is being proved. I don't know if Subset of Finite Dimensional Vector Space is Basis iff Linearly Independent iff Generator is too long. --barto (talk) 08:08, 29 July 2017 (EDT)