Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I have a subgroup [itex]S=\left\langle A \right\rangle[/itex] generated by the setA, i.e. [itex]S=\left\{ a_1 a_2 \ldots a_n \;|\; a_i \in A \right\}[/itex].

When I need to prove by induction onnsome property ofS, what should I choose as the base case of induction? n=1, or simply n=0 ?

If the answer is n=0, then it seems to me that in most cases associated with "subgroups generated by some set", we always have to define n=0 as corresponding to the identity element, thus the basis of induction will be always about proving that some property holds for the identity element. Am I right?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question on a proof by induction

Loading...

Similar Threads - Question proof induction | Date |
---|---|

I Proof of Existence of Tensor Product ... Further Question .. | Mar 17, 2016 |

Proof question: the sum of the reciprocals of the primes diverges | Jun 13, 2014 |

Question in Proof of second order condition with linear constraints | Jun 21, 2011 |

Orthogonality theorem proof method question | May 9, 2011 |

Question from the proof in euler's forumla | Mar 14, 2011 |

**Physics Forums - The Fusion of Science and Community**