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 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
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