Let 
be a subset of the nonnegative integers 
with the properties that (1) the integer 0 is in 
and (2) any time that 
is in 
, one can show that 
is also in 
. Under these conditions, 
.
Principle of Weak Induction
See also
Induction, Principle of Strong 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 Weak InductionCite this as:
Weisstein, Eric W. "Principle of Weak Induction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrincipleofWeakInduction.html