Fallacy/Examples/Arbitrary Example 1
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Example of Fallacy
| \(\ds x\) | \(\ge\) | \(\ds y\) | by hypothesis | |||||||||||
| \(\ds y\) | \(\ge\) | \(\ds z\) | by hypothesis | |||||||||||
| \(\ds \leadsto \ \ \) | \(\ds x\) | \(>\) | \(\ds z\) |
is a fallacy.
Proof
Let $x = y = z = 1$.
Then:
- $1 \ge 1$
which satisfies both $x \ge y$ and $y \ge z$, but it is not the case that:
- $1 > 1$
Hence the given argument is a fallacy.
$\blacksquare$
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): fallacy