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The inductive hypothesis is the temporary assumption made during the inductive step that the proposition $P(k)$ is true for an arbitrary integer k. It is used as a premise to derive the truth of $P(k+1)$.

Conditions: Used within the proof of the inductive step.; Assumes $P(k)$ is true for a fixed arbitrary k.; Required to prove $P(k+1)$.

The inductive hypothesis is the temporary assumption made during the inductive step that the proposition $P(k)$ is true for an arbitrary integer k. It is used as a premise to derive the truth of $P(k+1)$.

Conditions: Used within the proof of the inductive step.; Assumes $P(k)$ is true for a fixed arbitrary k.; Required to prove $P(k+1)$.