dimension of the vector space spanned over the rationals, and odd zeta values.

Hi guys,

I'm reading a fascinating paper on the infinitude of zeta values of the form $\displaystyle \zeta(2s+1)$. Whilst I understand the whole idea of the proof, and a fair bit of the detail, there's one vital part that's bugging me. The paper starts off with the following line: "We provide a lower bound for the dimension of the vector space spanned over the rationals by 1 and by the values of the Riemann Zeta function at the first n odd integers."

That is, for every $\displaystyle \epsilon > 0$, there exists an integer $\displaystyle N(\epsilon)$ such that if $\displaystyle n > N(\epsilon)$,

$\displaystyle

\dim_{\mathbb{Q}}(\mathbb{Q} + \mathbb{Q}\zeta(3) + \ldots + \mathbb{Q}\zeta(2n+1)) \geq \frac{1-\epsilon}{1+\log(2)}\log(n)$

I'm a little uneasy with this notation, and I find it slightly confusing. Is there any other way you can put this?