A Solution to the P Versus NP Problem

According to conventional wisdom, the relationship between P and NP must be one of two possibilities: either P=NP or P≠NP. Unlike traditional approaches that base mathematical concepts on equivalent transformations—and, by extension, on the principle that correspondence remains unchanged—this theory is founded on non-equivalent transformations. By constructing a special non-equivalent transformation, I will demonstrate that for a problem P(a) in the complexity class P and its corresponding problem P(b) in the complexity class NP, P(a) is a P non-equivalent transformation of P(b), and P(b) is an NP non-equivalent transformation of P(a). That is, the relationship between P(a) and P(b) is neither P=NP nor P≠NP.