This algorithm (shown in the image) finds the element max in the matrix. This is a test for contradiction. Is this algorithm not tested when it reaches max> = A[j] in the last line of the second slide. Is what contradicts (2) even necessary? Because on the second slide you showed that max is in the matrix, and then fulfilled the condition of a maxium m: an element m of A such
that m> = A[j] for all 1 <= j <= A.length.
This seems to be two tests in one. And since it seems to me that the direct test occurs first, then the proof by contradiction is redundant and, therefore, is not necessary. Am I missing something? Is this just a test for contradiction? Or is it a direct test instead?