User talk:Lord Farin/Backup/Definition:Norm (Linear Space)

Does this really need a separate page from Definition:Norm? They seem to be the same. --Cynic (talk) 03:46, 19 February 2009 (UTC)

I think there's a plan by Cañizo to pave the way for disambiguation pages. I can understand the thinking behind it, but I'm anti this idea big time. If a user is following through a proof, comes to a definition he/she doesn't understand, and then has to work out which of several pages to navigate to, that's unreasonable. It should be up to the writer of the page to direct the user straight to the relevant page for that proof.

Alternatively, it could be due to a desire to separate the separate contexts of a definition (see the discussion on continuity). Again, I think this is a bad move unless (like, for example "closure") the definitions have nothing to do with each other (work in progress to rationalize this).

So my view is: get rid of this "disambiguated" definition and carry on doing it the way we've been doing it the last year or so. --Matt Westwood 07:28, 19 February 2009 (UTC)

No, this definition of norm is very different from Definition:Norm, notice that the latter needs a multiplicative structure on the space. The property $\left\|{x y}\right\| = \left\|{x}\right\| \cdot \left\|{y}\right\|$ does not make sense in a linear space. The contexts are very different: in functional analysis, Definition:Norm is never used. It seems to me that the latter is more common in algebraic number theory.

I really don't have any special idea on disambiguation pages, but these two definitions are indeed different.--Cañizo 11:59, 19 February 2009 (UTC)

By the way, the previous definition of norm was already incorrectly linked from Cauchy-Schwarz Inequality, so it may cause some confusion.--Cañizo 12:00, 19 February 2009 (UTC)

I understand about disambiguation pages better now than I did when I wrote the rubbish above. Feel free to completely disregard my communications on the subject on this page previous to this, and set up disambiguation pages as you like. Also feel free to use the paradigm that has been used on other disambigs, i.e. the "disambig" template. --Matt Westwood 20:34, 20 April 2010 (UTC)