Lemma: The Proving Principle by Contradiction 

Let \(p\) be a proposition and \(\neg p\) its negation. By showing that:
\[\neg p \Rightarrow 0\]
it follows that
\[p = 1.\]

This proving method is called by contradiction or reductio ad absurdum.

Formally, reductio ad absordum is the following logical argument: $$\begin{array}{rll}
\neg p\Rightarrow 0&\text{premise}&\text{e.g. It is false that the sun is not shining.}\\
\hline
p&\text{conclusion}&\text{e.g. Therefore, the sun is shining.}\\
\end{array}
$$

| | | | | created: 2014-06-22 09:22:17 | modified: 2020-06-24 06:16:08 | by: bookofproofs | references: [593]

1.Proof: (related to "The Proving Principle by Contradiction")