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]

[593] **Cryan D., Shatil S., Mayblin B.**: “Logic. A Graphic Guide”, Icon Books Ltd., London, 2001