Prove that $(\Bbb{R},+)$ is isomorphic to $(\Bbb{C},+)$.
I don't know how to proceed in this question. On doing a customary internet search, I found that this can be proven using Axiom of Choice. Does there not exist an explicit isomorphism?
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They both are $;\Bbb Q$ - linear spaces. What is their dimension? – Timbuc Nov 29 '14 at 13:55
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@Timbuc- How do I prove that they have the same dimension? – algebraically_speaking Nov 29 '14 at 13:58
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Take into account the cardinality of $;\Bbb Q,,,,\Bbb R,,,,\Bbb C;$ – Timbuc Nov 29 '14 at 13:59