S-Convexity Mysteries of Faith

When the initial premises of mathematical proofs are wrong, we cannot get a mathematical proof because the logical system we rely on, when doing Mathematics, is not Classical Logic, but a subset of Classical Logic, which is Mathematical Logic instead. In this way,  a value false for the antecedent cannot bring a true implication, and the possible proof originating in it cannot be told to be a proof. 

It is wrong because if you take alpha to be 0.1, beta to be 0.5, A to be 0.2, and B to be 0.3, the inequality does not follow from the premises. 

In this case, most people would not keep on reading the paper, since that is almost the first line on it that matters in the communication of the results.