The truth of an Infinite sequence of propositions for , ..., is established if (1) is true, and (2) Implies for all .
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.