##  [Induction on Number of Generators](/induction-number-generators) 

  ##  [Induction on Number of Generators](https://puremath.quantumdictionary.io/induction-number-generators-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A proof strategy that establishes a property for algebraic objects (groups, modules, algebras) by induction on the minimal or given number of generators: prove a base case for 0 or 1 generator(s), then show that if every object generated by k generators has the property, any object generated by k+1 generators reduces to a case with k generators.