Theorems that we can prove only by contradiction

kadejoset

kadejoset

Answered question

2022-07-14

Theorems that we can prove only by contradiction

Answer & Explanation

salumeqi

salumeqi

Beginner2022-07-15Added 15 answers

There are in fact numerous theorems that cannot be proved without arguing by contradiction. A nice example is the extreme value theorem (EVT). One cannot prove this theorem without an argument by contradiction, whose main ingredient is the Law of Excluded Middle (LEM). There are alternatives to classical logic where the LEM is not part of the package. Such logics are generally known as intuitionistic logics. It turns out that the extreme value theorem is actually false in one such setting. From this it follows that the EVT cannot be proved without LEM.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?