I'm currently reading through "A Book of Abstract Algebra" - C Pinter and have come across cyclic groups $$G = \langle a \rangle = \{ e, a_1, \ldots, a_n \}$$
Are there any cyclic groups isomorphic to $\mathbb{R}$?
2026-03-28 01:46:21.1774662381
Examples of cyclic groups isomorphic to $\mathbb{R}$
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Every cyclic group is countable. The group of real numbers under addition is uncountable. Therefore, the group of real numbers is not cyclic.