Double Reductio ad Absurdum
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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