True, at least assuming the axiom of choice. A Hamel basis of R or C over Q has cardinality of the continuum. Without the axiom of choice, I doubt that it can be proved.R %26amp; C are isomorphic as vector space over Q true/false?
I guess there are three collections:
R = reel numbers; C = complex numbers; Q = rational numbers.
They have the same features for addition and for multiplication. So the collections are isomorphic indeed. However 'vector space' makes it unclear, unless it is one dimensional. Then TRUE.
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