In strong induction i do not understand why lets say you proved the base case
Then you assumed that the statement is true for all n from 1 to k, where k is some number in N.
And in the induction step you need to use the truth of say k-2, so k-2 has to be in that range above which is true when k is 3 or greater, so you add two more base cases, n=2 and n=3.
What i do not understand is what if k=7 then we used the truth of the statment for n=5 which was not included in the base case?
So can someone explain to me what is going on in the base case and induction step of strong induction because i do not get it. THank you for your time