Hello Everyone.

While I was reading along in a book I came across this: It says the convex hull is

$\displaystyle co(\{ x_n : n\in \mathbb{N}\}) = \{ \sum _{i=1}^m \alpha _i x_i : \sum |\alpha _i|\leq 1\}$

The $\displaystyle x_n$ are vectors in a vector space and the $\displaystyle \alpha _n$ complex scalars. But from my understanding (and wikipedia verifies this) the definition of a convex hull requires $\displaystyle \sum |\alpha _i|=1$. Normally I'd just think this was a typo, but the text goes on to use the fact that $\displaystyle \sum |\alpha _i|\leq 1$. So are the two things equivalent or what? I can't see how they are. . Help please!