This is rather elementary but I'm struggling with a formal prove:

Consider this closed nested interval with Rational end points, the usual definition are:

Closed nested interval [an,bn] where an,bn belong to Q

sqr(an) < 2 < sqr(bn)

and [an+1,bn+1] is subset of [an,bn]

Prove the there is no x (in Q) which belongs to this nested interval.

Thanks

PS: Also if someone can tell me if there is a way use mathematical symbols and notations in your post