The truth of an infinite sequence of propositions 
for 
,
..., 
is established if (1) 
is true, and (2) 
implies 
for all 
. This principle is sometimes also known as the method of induction.
Principle of Mathematical Induction
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References
Apostol, T. M. "The Principle of Mathematical Induction." §I 4.2 in Calculus, 2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. Waltham, MA: Blaisdell, p. 34, 1967.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.Cite this as:
Weisstein, Eric W. "Principle of Mathematical Induction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrincipleofMathematicalInduction.html