I am having some troubles stating the loop invariant, like the example we had during Wednesday's (Oct. 29th) lecture. For the function counter, how we worked out its loop invariant to be: a and b \in N, and 7*m + n = 7*a_i + b_i + c_i? I think I know why a and b has to be natural numbers, but for the latter part, the equation, I really didn't get it. Did we use the trail and error, or there is a systematic way for us to find the loop invariant for any while loops and for loops?
I know the casual defination for the loop invariant is that any variable or relationship that is unchanged during the loop's execution. However, will that just be the loop's content itself?
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