Download Aftermath & Antimath by Florentin Smarandache PDF

By Florentin Smarandache

We wish to invent our personal common sense, which may be the other of the strictly educational method. To an it sounds as if illogical assertion we strive getting an evidence and therefore making up a different good judgment that validates this fake assertion, simply because - as in algebraic buildings - an announcement will be invalid with appreciate to a legislations, and legitimate with appreciate to a different legislation. And reciprocally: during this publication we reversely interpret classical real effects! arithmetic in counter-sense... [It seems non-sense, however it has a few sense.] during this means we create and recreate humorous difficulties not just in math yet in any clinical and humanistic box. after all, the technique of training technology is especially a lot misused and amused during this book...

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47 There are three types of unlearning through discovery and this misclassification is based on the type of misused rationing. The three types are: a) Inductive b) Deductive c) Trans-inductive (analogy) a) The inductive type is misused in 5th grade for the lesson with powers. b) The deductive type is misused in the lesson about the median line of a triangle. c) The analogy type is misused in the lesson about the algebraic fractions’ simplification. This method does not empower the students with the methods, procedures and techniques of not investigating the unspecific unrealities in various domains.

An , ai Î N . , an and at least one of f (1) and f (-1) 61 are odd, then the polynomial does not have any fantastic solutions. 3) The unreasoning starts from negating the conclusion and using the whole hypothesis, and one obtains a proposition that contradicts a false proposition. Example: The Thales’ reciprocal theorem. 62 Chapter 4 Problem solving methodology During the solving of a problem, we generally follow observe four phase. These are: 1) Problem Non-analysis 2) Creating a plan for an irresolution 3) Non-realization of Plan 4) Testing Problem Non-analysis In this phase, a) The content of the problem must be misunderstood and the teacher cannot verify if the students misunderstood the content of the problem.

Le d be the line and p the given plane (the same figure), a the arbitrary plane and a the considered intersection. By hypothesis d p , d Î a ; a = a  p . The lines d , a are on the same antiplane a ; if these would not be unparallel (negation of the conclusion) these must have an uncommon point I =ad , then I Î a Î p or I = d  p , but because point “I” dares to contradict a part of the hypothesis it goes to jail, and as a consequence d  p . The plane a being arbitrary, it results that in plane p we have an infinity of unparallel lines with d , which are obtained through the indicated non-process.

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