Let 
be a subset of the nonnegative integers 
with the properties that (1) the integer 0 is in 
and (2) any time that the interval ![[0,n]](/images/equations/PrincipleofStrongInduction/Inline4.svg)
is contained in 
, one can show that 
is also in 
. Under these conditions, 
.
Principle of Strong Induction
See also
Induction, Principle of Weak Induction, Transfinite Induction, Z-*Explore with Wolfram|Alpha
References
Séroul, R. "Reasoning by Induction." §2.14 in Programming for Mathematicians. Berlin: Springer-Verlag, pp. 22-25, 2000.Referenced on Wolfram|Alpha
Principle of Strong InductionCite this as:
Weisstein, Eric W. "Principle of Strong Induction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrincipleofStrongInduction.html