4.2 Irrational Method

When demonstrating the same thing, there is also this method of doing it. When p implies q needs to be demonstrated, we still assume the condition with assume p in the proof. Then we will deny the conclusion by stating assume not q.

        p implies q
         proof
          assume p;
          assume not q;
          ······
          thus contradiction;
         end:


And then we will lead from this and state thus contradiction. It means that a
irrational method was used. If we assume that it is neither p nor q, it means
that an inconsistency occurred.