# Cardinality of sets Q and R

• Apr 14th 2009, 05:14 AM
linda2005
Cardinality of sets Q and R
Hello all,

I need your help for this one , thanks :

prove that , the dimension between \$\displaystyle \mathbb{Q}\$ and \$\displaystyle \mathbb{R}\$ is infinite.
• Apr 14th 2009, 08:19 AM
Plato
Quote:

Originally Posted by linda2005
prove that , the dimension between \$\displaystyle \mathbb{Q}\$ and \$\displaystyle \mathbb{R}\$ is infinite.

Please repost the exact wording of the question.
The above us not meaningful.
• Apr 14th 2009, 08:30 AM
linda2005
I mean:
the dimension of \$\displaystyle \mathbb {R}\$ as \$\displaystyle \,\mathbb {Q}-vector\, spaces\;\$ is infinite.
• Apr 14th 2009, 12:30 PM
NonCommAlg
Quote:

Originally Posted by linda2005
I mean:
the dimension of \$\displaystyle \mathbb {R}\$ as \$\displaystyle \,\mathbb {Q}-vector\, spaces\;\$ is infinite.

that's trivial because a finite dimensional vector space over a countable field is countable but \$\displaystyle \mathbb{R}\$ is uncountable.