When we apply things inside of the same piece of Science, is that an application or an attempt to further investigate how the phenomenon we refer to behaves? We tend to think it is the latter. Coming from Brazil, we do expect Applied Mathematics to be something like foam that dissolves in the environment in record time, what they once produced at UNICAMP. It is applying the concept, no doubts about it, but we still saw that as Pure Mathematics, since it is all inside of Pure Mathematics in our Inner Reality (Pinheiro, 2016a). What he actually meant, he would later on clarify, was applying the concept of S-convexity to Inequalities, what obviously made immediate sense to us as soon as he said it. We simply went around explaining what it was and asking if they could imagine some utility. We did not hesitate: The faculty where we worked was an Engineering faculty. Drawing a line to split what is application from what isn’t is something very difficult to do: In 2001, Doctor Dragomir asked us to find applications for S-convexity. In practice, the theory is another, as they say everywhere on earth. We are sure some people could spend even an entire life talking about the beauty of a letter in isolation. There is what we would like to call theoretical utility of a concept and what we would like to call material utility: In theory, everything is useful, even a single letter in isolation. If we do have mistakes, we’d better fix those. We then have to think of the difference between assessment, isolation of mistakes, and correction of mistakes (three items) and boredom, imagination, and breaking rules (another group of three items): Perhaps Classical Logic is not as perfect as we initially thought it was. Rigorously, therefore, what we are about to study here is possibly a nonclassical system. Introduction One could think that if we change a small rule in Classical Logic, we have a nonclassical system, even because that is what we ourselves said in a previous text (Pinheiro, 2016).
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