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#7072 Dodano: 26-10-2013 23:46. Głosów: 5
That mathematics is thought to be consistent justifies the use of Proof by Contradiction.
In addition, Proof by Contradiction can be used to infer the consistency of mathematics by the following simple proof:
The self-proof is a proof by contradiction.
Suppose to obtain a contradiction, that mathematics is inconsistent.
Then there is some proposition Φ such that ⊢ Φ and ⊢ ¬Φ.
Consequently, both Φ and ¬Φ are theorems that can be used in the proof to produce an immediate contradiction.
Therefore mathematics is consistent.
https://docs.google.com/file/d/0B79uetkQ_hCKbkFpbFJQVFhvdU0/edit?usp=sharing
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In addition, Proof by Contradiction can be used to infer the consistency of mathematics by the following simple proof:
The self-proof is a proof by contradiction.
Suppose to obtain a contradiction, that mathematics is inconsistent.
Then there is some proposition Φ such that ⊢ Φ and ⊢ ¬Φ.
Consequently, both Φ and ¬Φ are theorems that can be used in the proof to produce an immediate contradiction.
Therefore mathematics is consistent.
https://docs.google.com/file/d/0B79uetkQ_hCKbkFpbFJQVFhvdU0/edit?usp=sharing