= Wirtinger presentation
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For a <knot diagram> with at least one crossing, take one oriented meridional <group generator> for every arc between consecutive undercrossings. At each crossing impose the <conjugacy> relation between the incoming and outgoing underpassing generators, conjugating by the overpassing generator with exponent fixed by the crossing sign. These generators and relations present the <knot group>.
One crossing relation is redundant, giving a <group presentation> with one more generator than relations. The redundancy follows by following the diagram's regions, or by applying the <Seifert-van Kampen theorem> to the crossing neighborhoods and projection complement. For a crossing-free <unknot> there are no crossing relations to delete: its presentation is simply $\langle\mu\mid\ \rangle\cong\mathbb Z$. This treats the zero-crossing case without claiming it has a redundant relation.
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