Double Reductio ad Absurdum

Proof Structure

Let $N$ be a real number.

Let $P$ be the proposition:

$\map P x = N$

that is, that a certain number $x$ is equal to $N$.

The Double Reductio ad Absurdum is an argument in the form:

$(1): \quad$ Suppose $x < N$.

Then it is possible to derive a contradiction.

Therefore $x \not < N$.

$(2): \quad$ Suppose $x > N$.

Then it is possible to derive a contradiction.

Therefore $x \not > N$.

So, because $x \not < N$ and $x \not > N$, it follows that:

$x = N$

$\blacksquare$

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): indirect proof
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): indirect proof