Talk:Metric (mathematics)

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[edit] Split metric space into metric (mathematics) and metric space

I split metric space into metric (mathematics) and metric space. Reasons were

• metric space article has become too long
• norm (mathematics) and normed vector space are separate articles too
• different metrics can be used to define the same metric space (depending of course on how one defines sameness)

MathMartin 12:27, 8 Apr 2005 (UTC)

I think this splitting up is a good idea, but more cross-links are needed between these two pages (and they should refer to precise sections and/or examples, so section titles should be well-thought).

I would only criticize a bit your last point: In mathematics, "the same" should mean equal, IMHO. "Equivalent metrics" are now defined, they define the same topology, i.e. the same topological space, but not the same metric space (defined as a certain 2-tuple).

— MFH: Talk 13:28, 19 Apr 2005 (UTC)

Section linking between articles is a very bad idea, because the links are prone to breaking. If section linking cannot be avoided the two articles should be merged again. What do you mean by same should mean equal ? MathMartin 13:44, 19 Apr 2005 (UTC)

[edit] bug fixes and cleanup suggested

1. in "Definition", it is written "function function" - should we just delete the first "function", or was it intended to replace it with "distance" ?
2. I suggest that at least "pseudo" and "ultra" should be defined in the same place than "intrinsic" (much more used, IMHO), i.e. in "Definition"
3. "Notes" (I would prefer "Comments") - here the last phrase (2,3,5 => 1) refers to a property "5" which is not defined ; please correct (and, if possible in 1 or 2 lines, write the proof).
4. The notion of 'metric induced by a norm' is already used 2 sections before(Examples) so there should be at least a forward reference (maybe better give the definition in a subsection of "examples")

— MFH: Talk 12:59, 19 Apr 2005 (UTC)

I recently split this article from metric space so most of the bugs are probably from me. I had intended to do a cleanup in the next few days. All your suggestions seem reasonable so go ahead. However I would keep the old section title Notes as it is more common in math articles on wikipedia.

As a sidenote, I think it is uneccessary to discuss such small modifications on the talk page. The next time you should be more bold and just do the changes. MathMartin 13:27, 19 Apr 2005 (UTC)

[edit] remove fraction

I changed

d_a( x, y ) = Σ a_i p_i(x-y) / (1 + p_i(x,y))

to

so I changed that a_i coefficent to a specific geometric series. That's what's in my book, and I guess it's needed to ensure convergence of this sum -Lethe | Talk 05:49, July 11, 2005 (UTC)