# Cardinality of sets Q and R

• April 14th 2009, 06:14 AM
linda2005
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.
• April 14th 2009, 09:19 AM
Plato
Quote:

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.
• April 14th 2009, 09:30 AM
linda2005
I mean:
the dimension of $\mathbb {R}$ as $\,\mathbb {Q}-vector\, spaces\;$ is infinite.
• April 14th 2009, 01:30 PM
NonCommAlg
Quote:

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.