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

["m7ossny"]

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!?


Thanks alot for time, Bye.