This is a question regarding the following statement on pg 43 of Atiyah's K-Theory.
Using our construction of $K$ it follows that, if $X$ is a space, every element of $K(X)$ is of the form $[E]-[F]$, where $E,F$ are vector bundles over $X$.
I don't understand this statement. $K(X)$ is the group generated from the elements of $X$. How are $[E]$ and $[F]$, or even $[E]-[F]$, elements of $X$?