Induction Principle

The truth of an Infinite sequence of propositions $P_i$ for $i=1$, ..., $\infty$ is established if (1) $P_1$ is true, and (2) $P_k$ Implies $P_{k+1}$ for all $k$.

References

Courant, R. and Robbins, H. ``The Principle of Mathematical Induction'' and ``Further Remarks on Mathematical Induction.'' §1.2.1 and 1.7 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 9-11 and 18-20, 1996.