Suppose a vector space $V$ has infinite dimension, $\dim V = \infty$. Is the cardinality of the basis of $V$ neccesarily countable infinite?
If a vector space has infinite dimension does $V$ then have a basis ? If one can specify a set of infinitely many linearly independent vectors is this set then regarded as a basis for $V$ ?
Are there results that can be proven for vector spaces with finite dimension, but not for vector spaces with infinite dimension ?
Why does most books on linear algebra only mention finite dimension vector spaces ?