I'll go strait to the point:
I have an array of values (it is a problem from CS but simplified) like :
indexing starts from 0. so A = 1
1 2 3 4 5 6 7 8 9 10 11 12 13 ...
rule by which the array if filled is : A[i+1] = A[i] +1
Question is :
Will the difference between two consecutive values always be 1.
I decided to prove this by induction on i. So, for i=0 we have A[i+1] -A[i] = A[i] + 1 -A[i] = 1 as expected. Then for i>0 according to the inductive hypothesis if p=0..k, A[q+1]-A[q] = 1 and for q = 1..k+1 we have A[q+1]-A[q] = 1 then it follows that for all i = 0..k+1, A[i+1]-A[i] = 1.
Does this make any sense ??