Cardinality of sets Q and R

Printable View

April 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 $\mathbb{Q}$ and $\mathbb{R}$ is infinite.
April 14th 2009, 08:19 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, 08:30 AM
linda2005

I mean:
the dimension of $\mathbb {R}$ as $\,\mathbb {Q}-vector\, spaces\;$ is infinite.
April 14th 2009, 12:30 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.

All times are GMT -8. The time now is 03:45 PM.