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Principle of Weak Induction


Let D be a subset of the nonnegative integers Z^* with the properties that (1) the integer 0 is in D and (2) any time that n is in D, one can show that n+1 is also in D. Under these conditions, D=Z^*.


See also

Induction, Principle of Strong Induction, Transfinite Induction, Z-*

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References

Séroul, R. "Reasoning by Induction." §2.14 in Programming for Mathematicians. Berlin: Springer-Verlag, pp. 22-25, 2000.

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Principle of Weak Induction

Cite this as:

Weisstein, Eric W. "Principle of Weak Induction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrincipleofWeakInduction.html

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