Proof by Contrapositive Is Wrong

1•slack3r•6mo ago

Proof by contrapositive is wrong. There is a true, false and undecidable case also.

Let me explain how it works.

p. =>. q. does not necessarily imply not q ==> not p. There are three cases here. If not q is true, then p can also be undecidable.

Comments

apothegm•6mo ago

If p is undecidable in that case, then p ==> q is false. The meaning of the statement p ==> q is that p is never true without q also being true.

slack3r•6mo ago

You have to first prove that p is not undecidable. This is not being done in many proof by contra-positive based proofs in mathematics. First prove that p is not undecidable is not a step in Analysis I by Terence Tao for instance.

FrankWilhoit•6mo ago

Which letter of "if" do you not understand?

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