TITLE: Does every vector space contain a zero vector?
QUESTION [15 upvotes]: If this is true, then every vector space must always have at least one subspace, the one consisting of only the zero vector, correct? 
Thanks!

REPLY [6 votes]: Every vector space also contains itself, and is its own subspace.
Except in one very special situation (which one?) it follows from this that almost every vector space has two subspaces.