The principle of induction states that:
Suppose\ that\ P(n)\ is\ a\ statement\ involving\ a\ general\ positive\ integer\ n.\ Then\ P(n)\ is\ true\ for\ all\ positive\ integers\ 1,2,3,...\ if\
(i)\ P(1)\ is\ true,\ and
(ii)\ P(k) \rightarrow P(k+1)\ for\ all\ positive\ integers\ k.
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