Set of vectors whose coordinates are integer (is a subspace?)

1. The problem statement, all variables and given/known data



For a set of vectors in R³,



is the set of vectors all of whose coordinates are integers a subspace?





3. The attempt at a solution



I do not exactly understand if I should be looking for a violation or a universal proof.



If x,y, z [itex]\in Z[/itex] then x,y,z can be writted as {(x,y,z)|x,y,z [itex]\in Z[/itex]}



(1,0,0) has integers as coordiantes but is not in the set because it does not pass through the origin.