can someone give me a hint on how to solve such questions in general ?

"Proof with complete induction that every number with with n element of Natural numbers, is divisible by 7"

thanks in advance

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- Oct 21st 2009, 07:46 AMcoobeComplete Induction proof
can someone give me a hint on how to solve such questions in general ?

"Proof with complete induction that every number with with n element of Natural numbers, is divisible by 7"

thanks in advance - Oct 21st 2009, 08:14 AMtonio
- Oct 22nd 2009, 07:41 AMCaptainBlack
Complete (or mathematical) induction is a method of proving an assertion is true for every natural number by first showing that the base case (that is or ) is true, then showing that the truth of for some implies the truth of . When we have done these two things we have proven for all .

Now look at Tonio's solution and you will see that it fits this proof method.

Complete induction is often taken as an axiom of arithmetic.

CB