Reply to post: Re: Interesting times

Boffins attempt to prove the universe is just a hologram


Re: Interesting times

>>You can prove a theory to be true by showing that it being false would lead to a contradiction.

Technically true (called either of the following ex adverso, reductio ad absurdum, by contradiction), however, might be quite problematic to build a whole theory with this method. It is certainly easier to prove a single theorem (statement) out of many the given theory consists of. In proving every theorem you of course can try arguing one at a time by contradiction. It concerns Physics, Math and other sciences.

It usually works best/easiest when alternatives to a statement are few (like finite/infinite, unique/non-unique, rational/irrational). Say, the proof of the Fundamental Theorem of Arithmetic stating that prime numbers are infinitely many, a well-known proof, ascribed to Euclid comes to mind as one beautiful example. Or in proving that sqrt(2), sqrt(n) are irrational, with n being a not perfect square integer. Similarly many existence and uniqueness theorems are proven by contradiction for uniqueness, but not existence.

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