Ivan Shishkin, Birch Grove

Subgroups of the reals

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Revision 754

7/31/2026, 1:17:20 PM · Ancient Tree

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Recorded titleSubgroups of the reals
Recorded typeDefinition
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1Every [[Subgroup|subgroup]] of $(\R,+)$ is either [[dense|dense]] in $\R$, or [[Cyclic group|cyclic]] of the form $a\Z$ for some $a\geq 0$.
1Every [[Subgroup|subgroup]] of $(\R,+)$ is either [[Dense subset|dense]] in $\R$, or [[Cyclic group|cyclic]] of the form $a\Z$ for some $a\geq 0$.

Revision 730

7/29/2026, 4:16:26 PM · Ancient Tree

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Every [[Subgroup|subgroup]] of $(\R,+)$ is either [[dense|dense]] in $\R$, or [[Cyclic group|cyclic]] of the form $a\Z$ for some $a\geq 0$.