Definition talk:Tangent Vector

There is a redirect from Definition:Tangent Vector to this page. But Tangent Vector needs its own page, not just a link to a page which contains the definition to that concept buried in another. Such is the philosophy of this site. --prime mover (talk) 20:02, 17 September 2014 (UTC)

Sorry for the mess, I was wondering whether you'd want that. Then this page needs to be merged with Definition:Tangent Vector, then Equivalence of Definitions of Tangent Space needs to be renamed into Equivalence of Definitions of Tangent Vector and the page Definition:Tangent Space needs to be recreated with a statement that it is the set of all tangent vectors. I can do the definition for the latter, but I am not acquainted enough with the site yet to do the refactoring. --Geometry dude (talk) 22:59, 17 September 2014 (UTC)

All of that, yes. Yes yes yes. Yes. --prime mover (talk) 05:06, 18 September 2014 (UTC)

Explanation

1) The derivative in the second definition is just a derivative of a function $f \circ \gamma  : I \subseteq \R \to \R$, so there's nothing special about it.

2) The Leibniz law is a special rule satisfied by so-called derivations. This belongs to abstract algebra. No, I am not going to define it, but I can remove this from the definition or give a link to a nonexistent page. The definition is complete and comprehensible as it is.

--Geometry dude (talk) 13:48, 22 September 2014 (UTC)

I'd rather you didn't remove the reference to the Leibniz Law. The template remains where it is for someone else to do that job if you're not up for it. The point is, it's a reference to a concept which belongs on its own page, and therefore we need a page to define it.

As for the question about the derivative, oh goodness me, what a dumbo I am! I think I'm going to have to put some words down somewhere to clarify it. --prime mover (talk) 20:22, 22 September 2014 (UTC)