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 . 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

, there exists an integer

such that if

,

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