Re: Is there a possibility to have more than one ZERO vector in a space!?

[Virgil]

In article <1162268294.384599.319130@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
 "m7ossny" <m7ossny@xxxxxxxxx> wrote:

> Hi,
> 
> I am not an Algebra Guru and have some question. Consider a metric
> space of vectors 'V' with a distance function 'd'. The vector space 'V'
> has a primary operator '+'. The problem is that I have to define zero
> vector where
> 
> 1. d(ZERO)=0.
> 2. v + ZERO =ZERO + v = v (for all 'v' in 'V')
> 
> Some times the '+' operator and 'd' function are complex enough that
> there might be more than one zero vector (a subset of vectors that all
> has absolute distance equal to zero). Some other cases there is a zero
> vector for each vector.
> 
> Does this sound right!? Or am I missing something!?

There is no more that one zero-vector per vector space, with or without 
a metric.