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geocalc33

16:13

checking in

7 hours later…

Shaun

23:10

Please could someone be generous with their time and give feedback on the following answer of mine?

A: Let $S$ be a subgroup of the group $\mathbb{Z}$. Then $S = \{ 0 \}$, else $S = \mathbb{Z}a$ with $a = \min\{ j \in S : j \in \mathbb{Z}^{+} \}.$

A group presentation for $\Bbb Z$ is $$\langle a\mid \varnothing\rangle.$$ This is because $\Bbb Z$ is cyclic, infinite, and generated by $1$, so all integer multiples (or, as in the presentation, all powers) of $1$ are in $\Bbb Z$ (or of $a$); presentations are usually multiplicative, but, here,...