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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,...