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