# Math Help - Cardinality of sets Q and R

1. ## Cardinality of sets Q and R

Hello all,

I need your help for this one , thanks :

prove that , the dimension between $\mathbb{Q}$ and $\mathbb{R}$ is infinite.

2. Originally Posted by linda2005
prove that , the dimension between $\mathbb{Q}$ and $\mathbb{R}$ is infinite.
Please repost the exact wording of the question.
The above us not meaningful.

3. I mean:
the dimension of $\mathbb {R}$ as $\,\mathbb {Q}-vector\, spaces\;$ is infinite.

4. Originally Posted by linda2005
I mean:
the dimension of $\mathbb {R}$ as $\,\mathbb {Q}-vector\, spaces\;$ is infinite.
that's trivial because a finite dimensional vector space over a countable field is countable but $\mathbb{R}$ is uncountable.