Hello all, I need your help for this one , thanks : prove that , the dimension between $\displaystyle \mathbb{Q}$ and $\displaystyle \mathbb{R}$ is infinite.
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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.
I mean: the dimension of $\displaystyle \mathbb {R}$ as $\displaystyle \,\mathbb {Q}-vector\, spaces\;$ is infinite.
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.
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