Currently I'm reading linear algebra books of leon's and friedberg's. In friedberg's book, for being subspace, a subset of vector space should (1). contain zero vector (2). closed under scalar multiplication (3). closed under vector addition
But condition (1) is missing in leon'book.
I think (1) is not necessary since if (2),(3) holds, then (1) must true
Does (1) necessary?
Thanks in advance.