Talk:Equivalence of Definitions of Tangent Vector

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My plan was to define the tangent space on a seperate page as the space of all tangent vectors. Any other suggestions? --Geometry dude (talk) 15:31, 16 September 2014 (UTC)

It's a definition, so it goes on a definition page. There's already a page for Tangent Space so those will need to be merged. Theorems and proofs about tangent spaces all go on a separate page for each one. --prime mover (talk) 17:04, 16 September 2014 (UTC)
Sorry, I forget the 'Definition:' prefix, when creating the page. Would you like to define tangent vector and tangent space on the same page then? The house style page does not state a policy regarding unnamed theorems, so I thought I would write them here as they clarify why the definition is the way it is and what these objects really are. --Geometry dude (talk) 17:39, 16 September 2014 (UTC)
There are plenty of useful guidelines, not only in the House Style pages. Start here: Help:Editing. But for the best way of getting to grips with how this site works, browse it. The structure as it has evolved is inflexible. While we are not completely shutting out all possibility of negotiation, developing pages structured to a different style without discussing that style first is likely to result in those pages being (at least) plastered with maintenance templates.
As for the fact that there is already a page defining "Tangent Space", I will leave it up to you to do the appropriate research to determine which (if either) of the definitions are the "correct" one. If they are both "correct" in their particular context (bear in mind that different streams of development may have devised different definitions and called them both by the same name) then both definitions are needed on $\mathsf{Pr} \infty \mathsf{fWiki}$ with the appropriate information included as to which context the definitions are valid.
Definition:Tangent Vector does still need to be defined, and that, as should now become apparent, needs a separate page to present it on.
Theorems need to state no more and no less than the result being stated and proved. Please do not fill up the section of the proof where it states the result with the details of what the various objects are that it concerns, beyond the entirely necessary links to the pages which define those objects.
Theorem statement section:
"Let (some notation) be a (such-and-such object, with link).
"Let (thus-and-so) equal (some particular case, with link if appropriate).
"Then (Statement of result)."
Proof section:
"By definition, a (such-and-such object) has (this-and-that property).
"So, by (link to theorem concerning this-and-that property), etc. and so on."
We believe that this style of presentation ensures the maximum clarity with the minimum clutter, and thence the best collection of expositions in the world as it exists today. --prime mover (talk) 19:17, 16 September 2014 (UTC)