Talk:Reverse Triangle Inequality/Normed Vector Space

Why is the special case for $0$ required? Surely all that needed to be done was to invoke the clause about the norm inducing the metric space, and that should cover all instances of elements in the domain, including when $z = 0$.

Incidentally, if $X$ is a general normed vector space, is it even accurate to state that $0 \in X$ at all? Strictly speaking, unless carefully specified, the conventional meaning of $0$ is as an element of a number field, although recognises that some sources use $0$ as the symbol for a general Definition:Ring Zero. From my limited understanding of vector spaces, in this context $0$ would be the Definition:Zero Vector. It would require to be stated as such, probably (according to site convention) denoted $\mathbf 0$. --prime mover (talk) 05:25, 9 May 2013 (UTC)