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
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.